having played HE almost exclusively i can say that lizardmen as scary. Terradons can drop rocks on our swordmasters, we cannot get guaranteed breaks from saurus and skinks are just a pain, kill our eagles which we dont like. Stegs hurt because impact hits go first.
An odd trick against HE is that you never want to charge them with your saurus. I guess its not that odd, just perhaps counter intuitive. You especially never want to charge spear elves or sword masters. the first looses a lot of its advantages if it charges. And the second will kill your entire front rank so you need the second rank to be able to do something.
Magic missiles really hurt HE, so death is not a bad lore. Otherwise use beasts and cast beast cowers as often as possible on princes or on the dragon. Probably not metal because he has low saves, or they will be immune to fire, and death is probably just better overall than fire.
Against phoenix guard i would imagine suarus would work well, same as against white lions. Try not to let dragon princes hit your flanks, and a burning alignment or two will kill many... many of them.
White lions are going to be somewhat hard to kill from shooting as they have a 3+ save. But they only get a 5+ save from magic missiles. PG are always just a pain to kill, but i would imagine the sheer number of attacks should get through the PGs ward saves.