Is there a limit to how late a lock_time can be set to?
The maximum value you can set for the nlocktime is 4,294,967,295 (0xFFFFFFFF in hexadecimal system)
That's equivalent to February 7, 2106 6:28:15 AM.
If not, suppose I send out a transaction that's time-locked to 1 day/month/year/decade into the future.
it may worth mentioning that nodes reject any transaction with a locktime into the future.
If you have a transaction with a locktime into the future, you have to wait until its locktime and after that you will be able to broadcast it.
In particular, do later-time-locked transactions need higher transaction fees in order to keep the same probability of being included in a block at t ≥ lock_time?
We don't know how much fee rates will be required for getting confirmation in the future.
If the fee is low, as mentioned above by Charles-Tim, you will need to do CPFP after broadcasting the transaction in the future.