Does the will to live cease after enlightenment?
"Ceasing the will to live" sounds depressingly suicidal. That's not a good description.

Dhammapada 203-204 describes Nirvana as the highest bliss.

You could say that the craving to enjoy life and, the craving to do or become something in life ceases.

When you look at your remaining years of life, and think that "in the next years or decades, I can travel to many countries, spend more time with my family, enjoy different types of food, build a career, become successful, raise my children to be successful etc." - well, that kind of thinking and emotions cease after enlightenment and is replaced with the peaceful bliss of the moment.