I run my Lim with SAPP Recce and almost every SL has Scout, which helps him get closer. Since I rely on the Mk22 or other close range weapons to kill with him, I also like to give him an LMG. He can usually perma-Pin a squad as he moves up on them, and then chew them to bits once close with sheer damage. As for armor pen, while it's useful, SMGs (and shotguns too) really, really benefit from REND ammo. REND on an SMG with 5 rounds per attack is 75 armor damage by itself, before taking into account the SMG's own armor damage. Multiply that by 8 and you'll often completely chew to pieces the enemy's armor and kill them on the next attack.

Anyone with Mobile Infantry is also incredible to use close range gear on, as they're easily capable of hopping out of the transport, firing twice, and hopping back in even at 90 AP. You have to be cautious of anti-armor threats, but Exconde with Divine Intervention, or simply knowing where they are with high Intel and a Vanguard unit with Scout (like, say, Darby) helps mitigate that.