How do you apply "Pick" to multiple sublists?

Try

Pick[lis1, Apply[Equal, lis1 /. assoc, {2}]]

An alternative to Pick, if I understand your parameters:

GatherBy[#, Map[assoc]][[1]] & /@ lis1

{{{A3, T3}}, {{A3, T3}}, {{A3, T3}, {A3, T1}}}