I assume there is plenty of fresh water available - and that the lambs can reach too? (Ie., not in a high-sided trough that they can't reach.) As they're on hay not grass, they'll need lots of water, and if the lambs can't access water then the only fluid they can get is mum's milk.
Are you offering the lambs lamb creep? Ie., highly palatable feed designed to make lambs want to eat it. At 6 weeks they really should be eating cake if its there. Otherwise, is it that the bigger lambs are hogging the lamb cake and these boys aren't really getting a crack at it?
If you can get them to eat cake then that will reduce the load on the ewe. And once they are eating sensible amounts, if she is still very thin, then you could wean them.
Yes I would certainly be making sure the ewe has plenty of cake. Depending on breed, 1-2lb per day. And if she's being crowded out from the trough by stronger ewes then yes, taking her to one side and feeding her on her own may be necessary.