There are three key areas that the Lizardmen can excel at when combating the Tomb Kings. However, before I go into these details I would advise that you get your hands on a copy of the tomb king list so that you are fully aware of the possible tricks that could be coming you way.
(1) Take a JSOD with a great weapon. I cannot stress the importance of this hero against most tomb king armies. Although tomb kings have tended to stay away from using heavy amounts of chariots with the profusion of str. 7 troops in the current edition, there will still be in all likelihood atleast one unit of chariots, if not more. With tomb kings magic, they can be surprisingly fast and effective as a flanking force to tip a combat. With a 18" charge, a JSOD can intercept chariot units and defeat them in 1-2 turns. Alternatively, you can have a JSOD version of an oldblood, so that you can take on chariot units that have a prince or tomb king in them with relative ease (although chariot mounted princes and kings have fallen out of favor recently)
(2) Load up on dispel dice. If you have a slann w/ a staff of sorcery and plaque of dominion (keep in mind drain magic is not useful against tomb kings so you can be comfortable with a 4th generation), along with a priest with a diadem of power, you should have a good mix of offensive power and defensive clout. Without magic, tomb kings are slow without particularly impressive troops. However, if their magic has free reign they become the exact inverse. Loads of dispel dice will see you through better than a few dispel dice, as tomb kings cast many lower-level spells, and the staff of sorcery will give you an extremely helpful +2 to dispel. Keep in mind as you go in to dispel primarily movement based spells (and if they have a casket, always reserve some dice for it as it is deadly against lizzies ld as it does not take into account cold-blooded), and do not be distracted by the magic missiles that he might throw around to draw out dispel dice.
(3) beware of tomb scorpions (and to a lesser degree tomb swarms). These units are perfect for taking out skinks, sallies, and the other units that play a crucial role in the lizardmen army. There tendency to pop out anywhere makes them harder to plan for, but a flexible approach when deploying you troops should get you through
Finally, I just have two minor pieces of advice that I find useful
(1) Focus on tomb king infantry blocks last. Your opponent wont be expanding the units as they would in VC, and with a low movement speed will probably not play more than a support role. Charging these units can bog down your troops for a dangerously-long period of time. If you take out the characters and faster elements of the list, you should be able to squeak out a win, so focus on those elements first.
(2) Although you may want to invest in a Tlazcotl for any Saurus you take, I would suggest not going overboard in your preparation. Remember that Tlazcotl prevents you from fleeing, and the frail nature of many of the tomb king shock troops makes baiting a very useful tactic.
