There are only a handful of units that have concurrent spring seasons for Mtn lion and Bear. Those units also have non-resident tags available at the discounted price of $41.75.
It is very unlikely that you will see a Mtn lion. However, if you think that the price is worth it, buy a tag just in case.
Out of the 449 lions killed in the 2014 season (last year with data), 114 were killed incidentally to hunting other species and 35 were killed using calling. Consider that over 100,000 hunters are in the mountains each fall for deer and elk and it looks like your odds of seeing a lion are 114:100,000 or 0.1%.
In addition, there are several wolf seasons that extend through spring bear season, check the seasons and if you are hunting in a unit with open wolf seasons buy a tag, $31.75.