My experience(as I try to know how to think as every faction) is Lyrans are fun because...you can play with people's
expectations.
If you have a two lance fight, for instance? Bring the classic line of Fafnir, Devastator, Atlas, and Thunder Hawk....
then throw in a Commando, Blitzkrieg, Hollander II, and a Starslayer.
Steiner, of course, is also known for their tank corps, and, in fact, in my Steiner Regiment I have been building, I have,
in addition to the tank battalion, a detached company that is for head-hunting duty.
If possible(and allowed in the scenario), you want to have artillery, preferably off-board Long Toms and Arrow IVs.
Steiner will fight either using a hammer and anvil type approach(their mediums and lights driving the enemy to break on
the line of assault 'mechs), or they use the "Wall of Steel": March the assault 'mechs abreast, pick one target, concentrate fire.
Always expect a Steiner to have at least one 'mech heavier then the rest. I have a recon lance, for example, that consists of
two Vindicators, a Centurion, and a Marauder. Also, remember: Steiners are Merchants...if they want something bad enough,
they can and WILL get it.
Steiner's inherent weakness, tactically speaking, is that, with the exception of the Blitkrieg and Stiletto, they tend to
be a little slower then other factions. Their assault lances you can either take apart via indirect LRM fire, or, better yet,
artillery. Otherwise, hit and fade, keep to cover, do not let them concentrate fire on you, isolate and kill them one at a time.
Expect to take damage, too.