Most effective way to figure out what will sound good under a lead melody that doesn't necessarily fit a specific scale?

I've been playing around with trying to compose some stuff, and I've been working on lead melodies. They typically don't necessarily fit within a specific scale, though, and that leaves me not really knowing how to approach composing rhythm guitar to go underneath it. Any thoughts on how one might most effectively figure out what will best work for rhythm, in that case?

submitted by /u/BardicThunder
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