Note: Although I have awarded the bounty of 50, this question is yet to receive an answer.

I won't award the 2nd bounty of 100 to anyone, unless ofcourse, someone posts a right answer by then (unlikely).

This a variation of this question by @Gamow

Suppose there are $100$ lions and $100$ zebras. The lions place themselves first on an infinite plane, and the zebras are placed next. Game proceeds turn-wise. On each turn, a single zebra or lion moves by upto $100$ metres. Lions win if a single zebra is eaten.

Zebras will try to ensure this doesn't happen. Do the lions' have a strategy that works irrespective of the zebras' one?