Aha! Now THAT sounds more like a LM army

.
First off, tell your friend to check the BRB FAQ. It states that killing blow works on a character regardless of the mount he is on. (p.6 it's on the gamesworkshop website)
There was confusion on that, but GW cleared it up.
You can check the entry on killing blow to see the specifics, but ours doesn't work on monsters, but it does on characters riding monsters (provided that they are a unit type that is subject to KB, which skinks are

). It works on war beasts, infantry and cavalry. If they have that in their entry, they are subject to KB. However, KB isn't 100% necessary since skink priests are T2 and 2 W. They do have a 2+ armor save though, so high str is still useful, but I've been able to topple one fairly easily without KB since they take so many wounds. Just a vamp or WK inside a unit should do the trick (4 str = wounds on 2+, just use R&F to finish the job).
25 unit saurus is pretty hefty still. That's 325 points per unit if he's using spears (which I imagine he is), so I'd handle it about the same as described. Fortunately, he doesn't seem to think that Saurus are more effective deployed in ranks of 6 instead of 5 (giving them a lot of extra attacks thanks to being in base contact on the corners). I wouldn't let him in on this. Be aware that he still will get 20 str 4 attacks coming at you (10 for first row, 5 support and 5 for spears).
If he deploys Kroq (which once again, he shouldn't be able to

) and engine of the gods, then he has over 1k points tied up in two models. That means he can't deploy TOO many army models, which is generally good news for you.
As far as how to handle the enginer of the Gods, I don't know what you know about it but it has a NASTY magic ability that hits undead with 1d6 S5 hits (no armor save) to all units within 2d6 inches. It goes off for free during his magic phase without the ability to dispel it. That's the biggest danger of it for us. Obviously this means keep it away from large groups if possible. As that is not always possible with our army, then I recommend the alternative of just killing it quick (discussed later) If the stegadon charges you, then you take 1d6+1 S6 impact hits, which also hurt pretty badly. The skink is usually effective level 3 as well. That's about the worst of it (there's more to it than that, but that's the need-to-know parts). He may "forget" (as my friend often does) that an engine of the gods stegadon does not come with crew (look under the engine of the gods box where it says howdah weapons are replaced in his book if he challenges that p.55). so he cannot use any blowpipes or ballista or anything.
It has weaknesses though. First off, as you probably figured, charging it will give you a lot of advantages. You negate the impact hits and if you charged from out of the range of the magic ability, then you deny him that as well. On the other hand, if he charges you he gets impact hits and during his magic phase his explosion will hit whoever is in contact with him (and anyone else who is nearby). Taking the book of arkham (bound danse spell) or a
necro with danse is one way to give you an edge in charging. Using cavalry could also work if you want to take them (although make sure you have enough to deal 2 wounds!). FYI it has a movement of 6.
Finally, kill the skink and the engine stops. As I mentioned, you are 2 wounds away from shutting it down. Sure, you may have a frenzied stegadon on your hands, but at least he won't hit all your units with a S5 no armor save attack.
One build that worked amazingly well for me (for your consideration only) is a thrall with AoD (GW) and infinite hatred. He had either flayed hauberk or some ward save for protection or something else I can't remember. With str 7, the stegadon had no armor save (they are at 3+) and was wounded on a 3+. It gave all the CR I needed (with the R&F units shredding the skink) to put him ldr 2 and run him down. To emphasize, I'm not saying this build is necessary just one I found helpful and is food for thought.
Also ancient steg has init 1 so you know purple sun could work for him too, although personally I would save it for the actual units (as a luck roll of 1 would negate your spell for the steg, but against a whole unit, he's unlikely to roll 25 1's

.) If he's in the way though, no harm in giving him a good blast.
As to your earlier post, Lord of Death can work fine on a thrall. The only advantage to giving it to your lord that I can think of is that it would be harder to dispel (it's a 3+ to cast either way), but I think the combat Lord benefits too much from infinite hatred to deny him that for lord of death. Replacing AoD with flayed hauberk is very common, the only downside to it is that you would deny other thralls of that item, but if you weren't planning on giving it to them anyways, then why not right?

Point is it's not a mistake by any means to do so, it's just a personal call on what you think is best.