Not at all, but you will be signing into Lightroom in order to take advantage of the future upgrade to LR 6.
You won't lose the program, but then it will revert to a trial edition and after the 30 day trial you won't be able to use the software.
…in other words, you will never, ever get to own the program. You stop the payments, the program ceases to work immediately.
Some would say that does amount to "losing" the application.