No Issues, probably...
Nystul’s Magic Aura is a utility spell that will solve exactly as many exploration problems as you (the DM) put into the adventure for it to solve. It does not contribute to combat ability in any way that I can see. In this way, giving a warlock access to NMA is not going to upset the balance of your game.
There are a few reasons why you might want to not do it, or at least not without a cost.
One of the reasons for different spell lists for each class is to make them each feel unique. Utility spells like NMA are a signature of the wizard class. Some people choose to play a wizard specifically because wizards get spells like NMA, so giving it to another class lessens the desirability of choosing a wizard. Does this matter for your campaign? If another player already has a wizard for their utility as a backup if their current character dies, then it absolutely does. If wizards are detested by every member of the group, then it absolutely does not.
Another reason (also of variable importance) to not acquiesce to the request is that it could make the players choice of warlock less meaningful. Choosing to play a warlock means choosing the limitations that accompany it. Having your cake and eating it too may sound fun to a player, but often just makes a game bland. I really doubt that this single house rule would cause this problem, but if it caused every player to ask for something similar, it could quickly add up to a problem. Ask yourself if this is a concern for your group.
An easy way to mitigate both of these problems (if either is relevant to your group) is to attach a cost. The simplest one that comes to mind is to utilize a feature of the warlock class that is already present and similar. The hexblade patron already grants additional spells to the warlock list. By swapping one of hexblade spells for NMA instead of just adding NMA in addition, you would be following a mechanical precedent of patrons granting access to otherwise class-unique spells, and also shows that you're not inclined as a DM to grant every exception requested, thereby avoiding the me-too's.
In conclusion, adding NMA to this warlock's spell list is a good idea, but adding a cost or limitation is worth considering.