There is always the risk with any vaccine that pups/dogs can have a reaction to it, Lepto is a vaccine that seems to have the highest reported amount of bad reactions, the side effect if your pup/dog is unlucky enough is an anaphylactic reaction, causing vomiting and collapse, usually shortly after the injection. They can also get an allergic reaction, causing hives and facial swelling, up to 12 hours after the injection.
I agree it is a coincidence that the pups are falling ill, it may well be a reaction to Lepto it does happen and vets should not shy away from the possibility and your friend should make sure she reflects her suspicions, as any reactions need to be reported to the company,
Out of interest, why did your friend wish to vaccinate the pups at 6 weeks? The mothers natural immunity via her milk can make vaccines this early irrelevant and not work at all, far better to wait until at least 8 weeks for the first vaccines, did her vet disclose this?
I hope that no more deaths occur, trouble with pups they pick things up so easily.