I thought it was because she shot it and killed it and I guess finding out that she was clear of cancer suddenly made her realise that she had taken a life (albeit a possum's) and brought home the reality that she was acting irrationally and out of character?
Earlier Lynette had ranted that the possum had invaded her home and it was her job to be there to protect her family etc etc . This was when her husband realised that she was equating the possumwith the effect of her cancer on her family and when he understood what was happening he let her get on with trying to kill the possum. Once she rceived the all clear Lynette understood her own motivation and "apologised" to the possum. Very moing stuff and brilliantly played
She was hell bent on killing this possum for rooting up her garden and succeeded in the end.
When the doctor came and told her she was in remission from her cancer, I guess she felt she'd been given a second chance at life and felt guilty and ashamed she'd robbed this animal of it's life.
I agree with Jeth I also thought that she was comparing the invasion of the possum with the cancer in her body. It had invaded her home as the cancer had invaded her. She killed the possum and then got the all clear.
It was very emotional. I think Felicity Huffman has acted brilliantly through these episodes.