Avi
“on the other hand we say “Modim anachnu lach”. “lach” is the feminine “you”.”
Not quite. (in fact the very next word is “sheatah”) the reason why it is “lach” is becasue it is a quote from Divrei Hayamim 19:13. There it is lach since by an esnachta LEcha becomes lach (occasionally by a zakef katan too).