My mother (94) is a Florida resident. She has been living with me in Illinois. Do we need to contact an Elder lawyer in Florida or Illinois?

Probably both. Where she will actually live her remaining life may be here residence and where her estate will be probated. if she has property, especially of value, like a condo, or investment fund, you may want to keep those things in FLA as they have no inheritance tax down there. If there are considerable assets in FLA I would consult with a FLA attorney. They are familiar with snow birds and those who are looking for tax advantages.