I think this is a case where the MUL may be helpful, but only to a degree:
http://www.masterunitlist.info/Era/FactionEraDetails?EraId=14&FactionId=32There you'll get everything Lyran, but not 'general'. It does not make the distinction between what is seen as being typically Lyran versus what they just have access to. So I'll throw some suggestions in. I don't know where your iconic 'Mechs stop, which may make some of these duplicates of what you've already picked up.
Fafnir - 100 tonner from 3067. 2x HGR. That's all you need to know.
Battle Hawk - 35 tons from 3055; a slower light, good for supporting heavier units.
Barghest - 70 ton quad from 3060. Every variant packs a BFG.
Goliath - 80 ton quad from Project Phoenix. Two solid Lyran variants.
Bushwacker - 55 tons, from 3058.
Razorback - 30 tons, from 3067. Decent light, the variant is nasty.
Blitzkrieg - 50 tons from 3060. Hunchback on speed.
Talon - 35 tons from 3058. Combines a Locust and a Panther...
Wolfhound - 35 tons from 3050. Tough, go-to light.
Nightsky - 50 tons from 3055. Yeah, it's got an axe.
Axman - 65 tons from 3050. Bigger axe.
Defiance - 75 tons from 3075. Warhammer-Marauder cross-breed.
Salamander - 80 tons from 3055. Archer's big brother.
Hauptmann - 95 ton omni from 3060. When you need a brick...
Berzerker - 100 tons, from 3055. Even bigger axe.