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There is some confusion on what the rules are for picking a lock. It all depends on whether or not you have a set of thieves tols and if you know how to use them. There are six different possibilities.

1. Add Proficiency Bonus To Damage
2. Do You Add Proficiency Bonus To Damage

1. You have Thieves’ Tools and are proficient with them. You can attempt to pick the lock and get to add your proficiency bonus to the (Dex) check.
2. You have Thieves’ Tools and have expertise with Thieves’ Tools. You can attempt to pick the lock and get to add twice your proficiency bonus the (Dex) check.
3. You have Thieves’ Tools but you aren’t proficient with them. You can still attempt to pick the lock but you don’t get to add your proficiency bonus (since it’s a bonus you only get when you are proficient with something).
4. You don’t have any Thieves’ Tools so you improvise some (with your DM’s approval) but you aren’t proficient with Thieves’ Tools. You can still attempt to pick the lock but with disadvantage.
5. You have improvised tools and you have proficiency with Thieves’ Tools. You have disadvantage on picking the lock, but you do get to add your proficiency bonus.
6. No Thieves’ Tools and no improvised tools. Take a strength check to throw the closest party member through the door or crowbar the lock. Basically, look for another way to get past it because you can’t pick it.

From D&D Wiki

When you do so, the monster’s Saving Throw bonus with that Saving Throw is equal to the Ability Modifier plus the monster’s Proficiency Bonus. Should you do this? The DMG suggests you do it to bolster a low Ability Score, but frankly, I think that’s actually a bad suggestion. Remember that players are attentive.

Proficiency Bonus

Characters have a proficiency bonus determined by level. Monsters also have this bonus, which is incorporated in their stat blocks. The bonus is used in the rules on ability checks, saving throws, and attack rolls.

Your proficiency bonus can't be added to a single die roll or other number more than once. For example, if two different rules say you can add your proficiency bonus to a Wisdom saving throw, you nevertheless add the bonus only once when you make the save.

Occasionally, your proficiency bonus might be multiplied or divided (doubled or halved, for example) before you apply it. For example, the rogue'sExpertise feature doubles the proficiency bonus for certain ability checks. If a circumstance suggests that your proficiency bonus applies more than once to the same roll, you still add it only once and multiply or divide it only once.

By the same token, if a feature or effect allows you to multiply your proficiency bonus when making an ability check that wouldn't normally benefit from your proficiency bonus, you still don't add the bonus to the check. For that check your proficiency bonus is 0, given the fact that multiplying 0 by any number is still 0. For instance, if you lack proficiency in the History skill, you gain no benefit from a feature that lets you double your proficiency bonus when you make Intelligence (History) checks.

In general, you don't multiply your proficiency bonus for attack rolls or saving throws. If a feature or effect allows you to do so, these same rules apply.

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Add Proficiency Bonus To Damage

Do You Add Proficiency Bonus To Damage