A friend of mine was diagnosed with cancer and as the disease progressed her needs changed. Then again, she lived alone. Also assuming your neighbor is female.
These are some things I did with/for her:
pet care
bathroom cleaning
gardening
snow removal
ran errands
picked out and decorated a Christmas tree
watched movies
read a book while she napped
helped give out Halloween candy
a neighbor actually brought her harp and played for her
secretly folded hotel corners on the toilet paper in all bathrooms - made her
It doesn't have to be a lot. Maybe ask to come over and be prepared with a list of suggestions. Then ask their opinion. Maybe family will be doing more personal care things, but pet care is daily and a big item. Changing the decorations as seasons come and go while she directs is good. Not too much of a commitment time wise, but a good companionship visit. She can give as much input as she feels able to.
Sometimes just sitting in the house reading while the spouse gets some away time to get refreshed is welcome. Or actually reading to the invalid the old fashioned way is quite pleasant.
Do be prepared for a change in yourself. I was not that close to my friend but as we shared the journey together ( and I was NOT the main helper ) she claimed a big chunk of my heart. I realized it was happening and the pain it would cause ( she was told maybe three months, but hung on for thirteen- even appearing on stage in our theater group about month five ), but it was worth it.
One more thought - offer suggestions ( Would you like chrysanthemums planted out front? Yes? Here are the colors I saw at the store, what do you like? I'll put a lawn chair out by the garden and you tell me where you want them.) Give her as much control over things as possible.