If the other ship that Manaroo is passing a TL to already has a TL on someone else, does that ship keep both TL's, or does he loose the one he has before Manaroo passes him a second?

They would have to discard one of the blue TL tokens they have. It doesn't have to be the one they started with, but when they are given a second, they have to discard one. (unless they only had one AND had weapons engineer)

It is actually a bit unclear when you assign the blue TL marker to another ship, Which one to discard.

When acquiring a TL you discard the old one for the new.

Other random manaroo target lock fun: you pass red target lock tokens to your ally too!