They can. It's a little bit tricky, though, because accounting for a third faction that's hostile to the other two simultaneously is something the AI is only at about 90% on. It's usually pretty good but sometimes it goes sideways.But "distract the Lost and/or use them against Advent" is not only possible, it's supported gameplay. You can research a grenade that lures the Lost to its location when detonated, which means you can do things like have the horde swarm a pod while you leg it in the other direction.
The Lost can actually be a ton of fun. I mean, you still need to treat them with respect, because they can and will murder you if you play sloppily. But the way the game works is that they die very quick and when you kill one you get to keep shooting, so it's entirely possible to have turns where two guys rip their way through about twenty of them if you have certain "reloading is free" abilities and gear.
And in a game that's so, so often about carefully calculating one-health-bar advantages and needing multiple guys to handle a pod of three enemies in the most efficient way possible or fighting Sectopods and Andromedans that absorb godawful amounts of punishment, it is just really fucking nice to occasionally fight things that simply die when you shoot them. You pull the trigger and they fall down! How novel! It's like being on zombie vacation.
-Merc
Keep Rat