This year I am feeding all my orphans on unpasteurised, unhomogenised Jersey milk. So far (oldest lamb 4 weeks) the only problem has been the change of diet back to sheep's milk if I get a chance of fostering a lamb that's been on Jersey milk. They get a bit squitty for a day or two but soon get used to the new diet.
Many of the farmers around here routinely use cow colostrum for the first few feeds for a newborn orphan. I've used the lamb colostrum replacers in the past and found them very good, but this year have used cow colostrum. Too early to say if it's as good - certainly no problems at this stage.
I feed very new lambs 6 times a day, 4 times after a few days, reducing to 3 times at about 2-3 weeks, twice around 4 weeks, wean (just stop) at 6 weeks - providing they are eating plenty of creep feed. Newborns get two feeds of colostrum, 100-150ml per feed if they will take it, 50ml tubed twice if necessary. After that I feed up to 1L per day split across the number of feeds they're getting, always stopping at each feed if the belly is getting bloated.
I do make sure to vaccinate lambs reared on anything other than a ewe. You have to take care to follow the instructions on the vaccine about the earliest to vaccinate, which will depend on whether it had any sheep's colostrum as well as which vaccine you are using.