That is a really old lemon tree but don't count it out just yet. I would remove all the fruit as that is a real power drain for a tree. Make sure you are fertilizing with citrus specific food 2 or 3 times a year.
Its time to think about how to 'replace' it (if it comes to that). Finding an arborist who could graft a few pieces to a new rooting system or sprouting some seeds are your best options.
There is a lemon tree at Logee's nursery that is over 110 years old and an orange tree in Oroville (CA) that is over 150 years old. There may be older ones but those are the two old timers I know of.