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So in D&D 5th edition, one can make a character with a background, e.g. a guild artisan who does locksmithing. Obviously a locksmith is very good at picking locks, even if he has no levels in the Rogue class. In this example, consider a guild artisan locksmith who becomes a cleric of Gond, god of craftsmanship.
The PHB doesn't get very specific, but a non-Rogue guild-artisan locksmith character who starts out might get (10 pounds of) "tinker's tools" or (1 pound of) "thieves' tools."
For adventuring, you could say that the locksmith just takes thieves' tools because they are lighter to carry, but probably that wouldn't be enough to construct a new lock, much less a new trap.
Assuming that the locksmith-adventurer plans to construct new locks (and possible new traps) while in a dungeon, presumably he would need to bring along lots of spare parts, and thus he would have to carry a tool kit at least as heavy as "tinker's tools."
Given earlier questions such as: Do you HAVE to have Thieves tools in order to pick a lock?
I suspect that the rules are not very precise about whether player-characters with a locksmithing background can construct traps while in a dungeon. From my guesstimate, I would say that they would need to negotiate with the DM to make sure the action is allowed in that DM's campagn.
Am I missing some clear rule on lock-and-trap construction, or did the rule designers just leave it open to interpretation?