I've had VERY good results breeding fish in a tank filtered by a sump, then growing out the fry in the sump. They outgrow fry raised in a 20 gallon by a lot.
Another thing to consider -- if you want to get a breeding pair of Lyonsi, unless you just get really lucky and buy a breeding pair somewhere, you'd prolly need to buy 6-8, grow them out, and let them pair off on their own. I don't know what size they'd be when that happens, but you could probably grow them out in a 125, let them pair up in the 125, and see what you have at that point.
If they're calm, stay kinda small because they're laying all the time, maybe they'd be fine in a 125. If they turn out more like mine were, buy the bigger tank, and keep fry in the 125 like you said.
Only problem with all that, though, is the other thing I noticed about the Lyonsi I had--he grew FAST. He outgrew all the Vieja I had growing in the tank with him. Like, he went from 4-5 inches to 8-10 inches in a matter of months.