Should I keep it as leading or can it still pick up when it is 6th Pokemon?
Pick Up is active which ever spot your Lillipup is in.
However, it depends on the level of the Pokemon with Pick Up as to what items you get. Lillipup also loses its Pickup ability upon evolving.
It does not have to lead basically.It can be any position(1st, 2nd etc) as long as it is in the party, pickup will work.