I just found out that the cantonal library in Lausanne (the one in Palais de Rumine, not the municipal library at Chauderon) launched an ebook lending service this week. It was about time! This has been a standard library service for years in North America.
They seem to have a pretty good selection of English novels (about 2,500). The platform is accessible here, but you need a library card in order to borrow a book (I already had one): http://www.bcu-lausanne.ch/bcul-numerique/electures/