HE cavalry with impact hits?!? Where did that come from? Simply ask him to point out the rule in his book which says they do, he will be sadly lacking since they don't.
The Lion Chariot.. Wow that is an interesting piece of work. It is almost twice the cost of the tiranoc chariot and essentially does the same job, I was at the forefront of the HE players saying it was useless for its points when the book first came out. Now I cannot count the amount of times it has had a massive impact on a battle and saved the day for me. From stopping a unit charging it through fear to inflicting massive casualties, and combining brilliantly with the fear causing Phoenix Guard to break units... Well, you don't want to hear that. The simple fact is even without the impact hits, in combat it is great, so you want to try to keep it out of combat.
Chariots still suffer from poison. Skinks have poison. Draw your own conclusions!
Also, if you flank charge a chariot, the beasts up front cannot attack. So your skink cohort actually has a decent shot at holding it in place: +1 flank, +1 outnumber possible +1 rank, possible +1 wound. Pretty sweet. Just make sure your general/BSB is nearby.
Unfortunately, LM don't have the best long range but that is usually where it can suffer. Try magic on it. The toughness is low for a chariot, it still is rather expensive, and has a pretty crappy save compared to most chariots. Point is, glass hammer. Hit it before it hits you. Golden!
HE elite infantry is really good now, but quite poor armour. Skink skirmishers are what you need, hit them with blowpipes or javelins from range and watch those swordmasters die in a hurry. Spearmen are ok, but as The Hunted said they will fall to saurus now.
A full unit of saurus spears will be able to stand up vs any HE infantry. Even swordmasters. Both sides will suffer heavy losses, but you have decent odds of holding/breaking/wiping them out. In any normal case, that (infantry) unit isn't going nowhere without help.
Dragon Princes are probably one of the toughest things you will face. Yes, after the charge they have s3, but 2 attacks and ASF with high WS is nothing to laugh at. Plus the horses get to attack. 6 princes will dish out 19 attacks including champ and horses, and the 2+ armour makes them tough. Granted, mine don't usually face saurus warriors, but against s/t 3 infantry, even without the charge they often win combat or at least draw, plus they have very good leadership to stick around. You want to get them clogged up with saurus, who they will struggle with, and possibly have a character in the unit facing them to eat them quicker.
Dragon princes are only a threat to saurus spears on the charge. After that T4 and S4 really comes to play. The massed attacks mean you cannot charge a Skrox unit in the front though. Always flank these boys. They have special armor, which makes him immune to all flaming attacks. Thus your Burning Blade of Chotec and the entire Lore of Fire is useless against DP.
Rest of the HE army... Well, it is balanced enough and not powerful so it really depends specifically on what your opponent takes and how he uses them. They must be used properly to win.
Repeater Bolt Throwers can be quite a pain, as are Eagles. The latter is just blowpipe fun, really...The RBT's are good fire support but only have 2 crew (who strike first!). Terradons/skinks of any sort/other support can hold them down and sometimes win.