Yes, absolutely! 

When lambs are born they are extremely vulnerable to the elements, particularly wetness or wind. They can cool down very quickly, lose their mobility and not get that all important first suck of milk, and before you know it ... a year's effort wasted (for that ewe anyway).

A good mother will turn, get up and lick her lamb, gurgling and talking while she is licking. Licking stimulates blood flow and the talking stimulates a response from the lamb. The lamb will try to get up and reach the teats for a suck. Good mothers almost seem to encourage this! 

The earlier lambs suck the better chance of survival they have. This is especially true with twins where there is a time the first lamb is on it's own while the ewe is having the second lamb. Good mothers don't ignore their first lamb during the process, continuing to talk and reach out to it while lambing the second lamb. However if the first lamb has already had a drink it's in good stead while waiting for it's sibling to be born.

Good mothers also stay close to their lambs and the place they lambed at for longer. There is research that shows this results in higher lamb survival. Ewes that talk to their lambs, stay close, and get them fed are less likely to lose sight of their lambs, or to have their lambs walk off in search of a mother.

So yes, absolutely, good mothering makes a big difference.

Does the ram make a difference how many twins and triplets he produces? Well, not really. Rams produce 100's of 1000's of sperm, more than enough to produce sextuplets every time, but they don't because it's not up to them.

Twins, triplets or quads are generally the result of multiple ovulation by the ewe. Some ewes produce more than one egg each time they come into heat, and if these make it to term the result is twins, triplets or more. Some breeds are more "prolific" (produce more offspring per ewe) than others, and this trait can be selected and improved by keeping the offspring of ewes that produce twins or triplets.

What role does the ram play? As we've said before, the ram provides 1/2 of the genetics to each lamb. If the ram has twinning in his pedigree, that is if his mother produced many sets of twins or triplets, his father's mother produced twins or triplets, and so on, then chances are very high that his female offspring will also produce twins or triplets. Since rams don't ovulate (produce eggs), we can't measure directly their twinning capability like we can in the ewes where we can see and count how many lambs they produced. So in rams we have to look at their female relatives to make inferences about their genetics for twinning.

If you want to produce twins, you need to keep the female offspring from ewes and rams that have twinning in their pedigrees, and in the case of the ewe that she produced twins regularly.

Another good indicator of twinning potential is early fertility. If a ewe produces her first lamb or lambs when she is a yearling, she is demonstrating early fertility. Many of these will go on to produce twins as 2 or 3 year olds and older. If a ram is born as a single to a ewe lamb, look at her mother to see if she has twinning in her performance history. Also ask about the ram's sire's mother to see if she has twinning in her records.