My son plays LM primarily and my primary army is Dark Elves, so I know the matchup. I would not say LM can't handle the normal DE builds. Plus you were not playing a maxed out DE build anyway. Realize that a bunch of 2 rank by 5 wide units of skinks can earn a lot of points off the witch elves and executions and other DE units and help cut them down in size before they finally get into combat. Positioning them at angles to the units, multiple skink units can shoot at the same time and kill a good number of models and then one unit can take a charge and get destoyed each of his turns. Salamanders are eseential but so is a good slann that gets off some magic. A fiery convocation on an executioner unit or witch elf unit even if a miscast eats 5 or 6 TG (assuiming a slann on a flank) is well worthwhile in messing up the opponent's next magic phase and really cutting down those witches and execs.
The DE army's best tools are magic (blade wind, word of pain and black horror are issues for your skinks and saurus particularly in larger units) and shooting. Repeater bolt throwers can do a lot of damage to monsters and Krox and TG and saurus, and repeater crossbows (dark riders and darkshards) can earn their points with shooting against TG and saurus. Using small skink units separated out will keep those spells from being as effective.
It really does help to start doing warhammer math and understand how things work.
Fiery convocation math: With a 5+ AS, execs will suffer a 2/3's wound rate and save only 1/6 of the wounds for a total loss rate of 55.56%. Warriors with shields suffer the same loss rate. Witches without the ward save simply lose 66.7% of rank and file models. Corsairs and dark riders with 4+ As and witches with 5+ ward save (with cauldron) will suffer unsaved wound rates of 44.4%. Plus once in play, the dark mage must use power dice or a displell scroll to dispel the spell in his next magic phase or lose even more models to the spell, which is really important in stopping DE magic coming back at you or forcing the DE mage with a lot of dice to risk miscasts to get something big off. You have similar math for soul quench hits, which you get 2D6 hits at a casting cost of 8+, and salamander hits (which can often get over 8 and as many as 10 to 12 models with a well placed and angled shot and good roll). Plus salamander flame hits and fiery convocation generally cause panic tests except if
You want javelins on your skinks for the extra armour save and parry save in case the DE player has repeater crossbow shooting on warriors or dark riders and for the ability to move/march and shoot with skinks and stand and shoot at very close range when charged. With T3 elves, improving the hit rate is worth more than poison and suffering a movement penalty and a double-shot penalty to the BS when shooting and you will almost always be moving and repositioning skink units for redirecting and blocking and shooting against dark elf armies. Also, effective redirecting and blocking means getting up close and blowpipes cannnot stand and shot if you are within 5" of the charging DE infantry unit with M5 (within 9" if charged by warlocks or dark riders due to their M9). Against execs and witches with a 5+ ward, 10 single shot javs cause 1.67 wounds per round of shooting at long-range and 2.22 unsaved wounds at short range. With stand and shoot, they cause 1.11 wounds at long range and 1.67 wounds (unsaved) at short range. That may not seem like a lot of wounds caused but the point is to set up the unit for magic damage and salamander shooting and to use multiple skink units to slowly deplete the unit to the point where the TG can ultimately fight it and destroy it or avoid that unit and take on and kill enough of the rest of the army to win overall.
With the parry save, 10 exec attacks on a unit of skinks with shields cause a total of 5.4 wounds. An exec army seeing LM should run units at least 7 wide to max hits and, in larger battles, 10+ wide to get an extra rank of attacks in as a horde. Without characters, that means 15 attacks with champ will kill on average 8.1 skinks and the skinks will be lucky to get any wounds back (hitting on 5's and wounding on 4" and then 5+ saves) but will be able to flee (difficult to rally below 3 models on double 1's even cold blooded) and force the player to not pursue (hoping you don't rally) and reform to avoid exposing a flank. If the unit is in horde formation, has characters or has frenzy, then 10 skinks will die before they get to hit back but the unit is heavily invested or worth delaying combat with.
Witches are another story, with 3 attacks each, poison and ASF (2 hand weapons and frenzy), they tear through skinks by causing so many wounds you really have no hoping of hitting back and forcing a pursuit. While 10 witches will only average 3.70 wounds, with three atacks across the front, they will generally get 28 or 29 attacks if 7 wide and more if horde.
Spearman, by contrast, do only 3.29 unsaved wounds per 10 attacks and tend to be run narror so that you may see as few as 10 attacks and as many as 15 attacks when they charge (no extra rank on the charge) and that means you will hit back some and maybe get a wound or two if lucky and still have a decent unit to flee with and have a chance of rallying. This is why we see corsairs with two attacks each and a better armour save of 4+ or darkshards (about as effective as spears in combat plus a parry save with shields and with great shooting ability) played over spears.
Realize that a TG unit will have some issues with executioners due to their greater weapon skill and S6 killing blow threatening any high armour save/multiple wound characters, but can win a fair fight with them. Execs have a narrower base which allows them to match up favorable with TG if they deploy more files than the TG unit and you will lose effective attacks from the slann taking up a total of 4 TG model spaces (2 in the second rank and 2 in the third rank). At T4, 97.2% of exec hits will wound and cut through the 4+ AS and 2/3's will hit unless you change the weapon skill balance with hand of glory on the TG or miasma (assuming you go for it) on the execs. That is 64.8% unsaved wounds per attack coming at you. In return, you will do a lot of damage on execs with 41.7% wounds per attack back and get effectively with PF 2.33 attacks per rank and file in the front rank to actually do more damge from the front rank than his front rank will cause but you will tend to have fewer supporting attacks that do proportionately less wounds and lose for that reason. The biggest problem is that the execs will cut down your unit and limit your supporting attacks. Get hand of glory on the TG or, miasma on the execs and the math will often flip with you hitting on 3's and him hitting on 4's. and you having more attacks in the front rank, then 10 exec attacks cause 4.86 unsaved wounds and 10 TG attacks cause 5.56 unsaved wounds back and you win as long as you have full attacks back. Cut the exec unit in half before it gets to the TG and you might lose the first round of combat slightly but will generally wiln every round after that due to the execs running out of models and ranks after your first round of combat. With stubborn TG, you can often combat reform to add files (go wider) to max front rank attacks to increase the damage rate on execs (with 2.33 effective attacks per model in the front rank) if needed.
Also note that DE spearmen will struggle against saurus because, even though they will get a lot of hits and re-roll to hit, they will wound far less and have difficulty cutting through armour unless the DE mage takes lore of shadow and gets off mindrazor on the unit. 10 attacks by spears on saurus only cause 1.48 average unsaved wounds. The saurus will hit less but have as many or more atttacks back (with 2.33/saurus in front rank) and much greater ability to wound and leave a minimal armour save. Thus, ten saurus attacks on spearmen will cause 2.78 average unsaved wounds.
Hope the math is right but should be.
Another note: the hydra is an issue for LM armies without a monster because skink shooting will only wound on posion hits half the time with the 4+ AS and then the new regen recovers half the previously lost wounds at the end of the opponent's turn. Lucky skink shooting combined with a good rolls on soul quench will sometimes do the trick and kill the hydra outright. But that sometimes means putting some wounds on the hydra and pulling it out of range of the generral in pursuit of skinks so that it cannot restrain pursuit at LD6 or avoid panics, etc. and then trying to finish it off with TG before he gets the thunderstomps and hope the breath weapon does not do much damage. You end up risking the TG unit being depleted to kill or break the hydra or losing a lot of saurus to a hydra to kill or break it. IN a larger points battle, a scar vet on cold one hits first and puts enough wounds to cut down the attacks back and saves most of the wounds anyway and no thunderstomps occur such that the hydra loses combat and flees or even dies due to wounds or is caught fleeing and dies.
Just watch out for the shades, they will likely try to pepper the salamanders with bolts 
