In the 5th edition, while the concept of alignment exists, its effects on the game mechanics is much more muted than the earlier editions. For paladins in particular, there are no requirements at all for them to follow a power at all.
But you are correct that in some earlier editions of the game, such as the 3e, the paladins of the Forgotten Realms setting had to choose a deity and that deity had to have an alignment of LN, LG or NG (page 25 of FR Campaign Setting 3e). However even under such strict rules, there were exceptions given, for example Sune, a CG power, had an order of LG paladins affiliated with her church.
So even if you decide to "immerse" yourself in some extra Forgotten Realms flavor of old (see footnote), and house-rule that the paladins should have a patron deity, it would be reasonable to let your player choose any deity of good alignment. (Or even one of CN alignment if the character's ethos agrees with that of the deity.) If the chosen deity is, say LG, you might even create roleplaying opportunities by considering his character as an unruly member of an order with mostly lawful paladins.
In short, given the lack of any constraints from the game mechanics themselves; it is up to you and your player to decide. I would personally recommend that you talk to your player and together you might come up with a nice solution that can improve your game. For a list of FR powers that support paladins, you might have a look at FR wikia's articles on paladins and paladin orders.
Note: According to Ed Greenwood presents: Elminster's Forgotten Realms:
Deities are paramount in Faerûnian life. Everybody believes in all the gods and worships every god... Only clergy, paladins, and fanatics specialize
in the worship of certain deities. Everyone else in the Realms is constantly poised between the gods, ...