This, as it turned out, is due to Lynn's resenting the presence of the real dog because she'd managed to convince herself that he was her husband's way of making her a slave to a slobbering brute. Given her nature, the longer Farley 'got away' with needing to be taken care of and being a reminder of the husband who she hated for leaving for no sense that she wanted to make sense of, the angrier Lynn felt. This means that fans who expected to see a Daisy or a Snoopy or even an Odie were left with a sort of furry abuse victim.
Since she could not challenge her sister-in-law directly, Beth simply stated that it would look bad to simply take the pooch down to the vet and have him put down because of bone cancer after all the crap he took and fed into Lynn's desire to be praised for her craft. Thus do we have a situation in which Farley looks good, people blame April for not listening to her parents and Elly gets to skate on having her head up her ass again. Mike's fitfully honest story about how he never did much for the dog when he was alive would lead to people figuring out who the error in the system actually was: a woman who cannot hold an object and walk at the same time because her brain is just a couple of neurons tied together in a slip knot.