One of the main premises of Buddhism is practicing detachment to posessions. My guess is that the Dalai Lama would not own a luxury wrist watch while his people suffer endless indignations in Tibet under Chinese rule.
Working with international relief organizations, I've been fortunate enough to have met some very high up lamas, though not the Dalai Lama himself. The thought of him or any revered lama owning a luxury item such as a watch is antithetical to who they are and what they represent. If I remember correctly, all the lamas I've met (a whopping three) have worn plastic digital watches if anything at all - usually a lama at a very high level has an extensive staff overseeing their schedule so they dont really need a time piece since they've got so many handlers. So while the Dalai Lama may enjoy working on timepieces (it would make sense since it would require much patience, which is also certainly required when meditating many hours a day), I'd guess he wears no watch or a cheap, basic watch, but JLC? I certainly hope not!