On average, what’s the most men a lesser house could field?

Tricky question. We know the minimum is around 1,000, from the text. The Florents have 2,000, the Karstarks around 2,700, the Pipers and Vances together have 4,000, etc – so 2,000 is more common. The Freys are notably powerful as a lesser House at around 4,000. 

In terms of absolute maximum, I think the Hightowers probably are the biggest lesser House, as they have a massive city to draw from as well as numerous important vassal houses. I estimate their numbers anywhere from 12-18,000 men.