The best replacement for mortise lock is cylindrical lock.

The best alternatives to mortise lock are rated as following:
★★★★★  cylindrical lock
★★★★★  deadbolt
★★★★  tubular
★★★  cylinder lock
★★  cylindrical
★  rim lock
★  electric strike
★  cylinder rlock

Your alternative for mortise lock is not listed? Suggest!
Speaking about mortise lock, one probably shouldn't forget about panic bar.

Other search terms related to mortise lock and their ratings are:
★★★★★ panic bar
You have in mind a companion for mortise lock and it is not yet here? Propose!



Google Trends

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mortise lock
cylindrical lock
deadbolt