N lions and M zebras on an infinite plain. Can we make progress?

The useful part

First the Lions choose their positions freely on the plane, then the Zebras do likewise. On the Lions' turn, one lion moves a distance up to 1 unit, then on the Zebras' turn one Zebra moves up to 1 unit, and so on. With 100 Lions and 100 Zebras, the case is still unresolved 11 years after first being posted here.

How it works

• Please refer to the following table Zebras $\downarrow$ Lions $\rightarrow$ $1$ $2$ $3$ $4$ $5$ $6$ $\cdots$ $100$ $\cdots$ $\aleph_0$ $1$ <t...
• including some involving an infinite number of animals of one type, or both.

Details worth keeping

This is a generalization of this question and this one. In both cases, and those below, the Lions and the Zebras act as two teams. Zebra, by ending its turn on the exact coordinates of that Zebra.