It is official forgotten realms lore than even someone praying to a gods domain can help give them some form of power... it has been heavily implied that prayer to Amaunator OR Lathander gives Lathander power either way... since he sort of IS Amaunator or at the *very least* took his job... people need gods for divine casting in Forgotten Realms...
Lathander is Amaunator has never been anything but a theory, though, and in-setting considered an heresy by Lathanderites. 4th Ed said they were the same but 4th Ed merged lots of deities (Talos and Gruumsh, for example, because that makes sense) and everybody hated that. When they walked back on that design choice in 5th Ed that was undone and they were made separate deities again. Amaunator was also one of the many gods who returned to life so now they're both around and divine at the same time.
Ah-ah-ah
Imma have to stop you there.
There is good reason that Amaunator worship in 5e is weird and foreign, or even considered outdated by much of the realm... The belief Lathander and Amaunator are the same is because they were separate for awhile... then in the era of 4e they became one but Amaunator took on a "good" alignment. Then the second sundering came and they were "separate" again.
They have a ton of overlap and prayer to both seem to work, even though the two faiths tend to butt heads...
*I* personally believe they are the same person but Lathander is willing to entertain both as that means all the more faith/prayer power for him.
Hell, some believe in the Heresy that the Sun is its own divine being meaning there are *three* sun gods.
Regardless, Lathander should be included in selection of deity at character creation.
