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'Lame' also carries pejorative connotations that portray, for example, Xiang Qi as an intrinsically poor game, which it is not. Stepping is a more politically correct term.

Returning to the main topic, obviously the attacking player's King would have to get close to the bare King soon enough to avoid the risk of such captures. What is more pertinent is that the crucial step of pushing the bare King back a rank or file would be impossible, as neither piece could even move to the rank or file along which the bare King was moving. A pair of Stepping pieces that moving odd numbers of ranks but even numbers of files, or a pair moving odd numbers of files but even numbers of ranks, could not force mate either, at least in a game where players strictly alternated moves. A game where players could make two moves at a time, but not with the same piece, is a different matter for such pieces, but that is not the kind of game on which this thread's 'number required to mate'.

The two kinds of piece that I invented in this comment (unless anyone knows better) are bound to alternate files and alternate ranks respectively, but their compound is the unbound full Rook. This is reminiscent of amphibian pieces, but as I understand it the term amphibian is reserved for where both component are symmetric.