In the commercial flock, we prefer to sell finished lambs straight off their mothers - less stress all round, and no growth check. In fact, in a good year we will get a few batches away have never been handled apart from ringing at birth.
Depending on the year we may wean in late summer and give the ewes a rest before going back to the tup. BH prefers to not flush and is very happy with single lambs (gives us an early crop and a heck of a lot less work), so there may be very little gap between weaning and the tup going in.
Very late weaned lambs don't seem to miss their mams, nor their mams miss them, so it's certainly less stress for them all than early weaning. And less risk of mastitis for the mothers too - not only are they not producing as much milk anyway, but also you are past the most nutritious stage of grass growth, so they are not getting pumped full of rocket fuel (causing more milk production, which can lead to mastitis if you've just taken the lambs off) if you leave them on good pasture.
I do want to stress that
lactation is not a contraceptive - there are no guarantees that a lactating ewe will not take the tup, so only leave entire lambs with their dams, or the tup running with the ewes and lambs, if you are happy to have the occasional accident.

(We do get a few some years, and don't mind.)
I would certainly replace milk with cake, at least for a few weeks, if I weaned early. .Weaning later, the lambs just carry on eating whatever they've been used to.