I have to say, I find that bottle-fed lambs do get this bloody froth as they get older and suck so very vigorously. In previous years I've used the bucket-with-teats setup (feeds 6 at a time) and have wondered whether this exacerbates the problem. Firstly the teats are made of harder plastic and secondly the lambs do have to compete with each other to get their share of the milk. (I do always make sure I put lambs together who suck at a similar rate.) This year I have acquired a 4-bottle rack, so 4 at a time get a measured individual feed and the teats are the soft 'non-vac' type. So far no bloody mouths, but my oldest is not quite 3 weeks old yet.
I never give any lamb more than a total of 1 litre of milk a day, split into however many feeds it's getting at the moment. And I take the bottle away / take them off the bucket as soon as their tummies start to bloat out. Some smaller types (mules, swaledales) never need as much as 1 litre, only ever seeming to need 750-800 ml. If a lamb seems not to be well-fleshed then you can always let that lamb have a few more sucks after it starts to bloat or, better, slip it an extra small feed. Fresh water is always available and they do drink a surprising amount - mind, I expect they spill a great deal of it splashing about!
I try to get mine out onto grass and into the sun as soon as I can. I seem to be able to get them to eat grass before they will eat hay. The first time out of the 'pet pen' is always a treat - oooh, look I can jump! Boing! And run! Scamper! And turn mid air! And pogo on the spot! (Yep, the treat is for me just as much as for them!)