Does that apply to any group? I know of a method that applies to the double scalar multiplication, but it speeds up Ed255119 only by 25%, at the cost of doubling stack usage.

Also, if a group has a structure that allows such speedups, I would fear that the same structure could also enable attacks… Ideally, you want your group to have as little structure as possible, that's what makes attacks infeasible.

Speeding 2x isn't enough to enable attacks when they already take exponential time.

It applies most commonly to curves with an equation of the form y^3 = x² + b which mathematically imply that (x, y) and (x, cuberoot(y)) are both points on a curve and so you can split a n bits scalar into two n/2 bits scalar and do double scalar multiplication.