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It depends on the LTO. There are LTO-1 through LTO-6 with 1 having the shortest service life and 6 having the longest. But that’s talking about end to end passes, not shelf life. You should expect anywhere from 9600 end to end passes for LTO-1 to 16,000 for most other LTO. You should be able to locate data specific to your tape drive in its documentation.
If you are talking about shelf storage, count on 15-30 years depending on tape, although you will probably get more time (possibly much more) out of it if stored properly in a proper temperature and humidity controlled environment.