My farmer friend had a lovely attitude to vets' bills.
If an animal needs veterinary care, then it gets it. He didn't agonise, just got the vet and accepted the bill as a cost against the flock, not the specific animal. Yes of course he'd discuss with the vet levels of treatment, in which conversation the value of the animal, breeding life left and so on, would be considered. But no animal would be left in need of veterinary attention.
Each year he would review all his costs and if the veterinary expenses line item was overlarge, dig into it and assess why. Often we could identify a factor we could address. For instance, one year, there was a particularly high incidence of vet callouts to assist lambings. We investigated further, and all the ewes of a particular breeding to one specific tup had had very large lambs. some of them too large to get birthed on their own. So we didn't use that tup on that type of ewe again, and also took more care selecting a tup for them, and made sure we didn't overfeed them pre-lambing. (Ie., they went onto the roughest grass and had no cake unless skinny.)
It's harder to do as a smallholder because our numbers are smaller, but I have the attitude I want to like myself and be able to sleep nights, so I do the same as he did, don't even think about the cost of the callout at the time (except insofar as I'll take the animal to the vet if it won't make it worse to do so), and make decisions about future breeds, pairings, systems and so on as a result of this and previous years' vet bills.
I don't have a rifle, so I don't have the option of shooting an animal I judge unlikely to recover, so I call the knacker for them and ask for humane destruction.
I'm not saying the OP is depriving this lamb of necessary veterinary care; I can't see the pic well enough to judge. But personally, I do hate to hear or see the phrase "vet fees would be more than the worth of the animal", because even if that person would never deprive an animal of necessary care, the use of the phrase as part of our parlance implies an acceptance of an attitude to veterinary costs that I deplore.