After Lemon ascended to an Alicorn, there was a lot of talk about who she was throughout Equestria. Since she resided in the Crystal Empire as the student of Princess Cadence, she was familiar with the royal familiar but had never had a chance to meet the ruler of Equestria, Princess Twilight Sparkle. Of course Twilight was interested in meeting her as soon as she ascended, since she hadn't known another princess who had ascended in her life time and she felt a strong kinship to Lemon for that fact.
Lemon was deathly nervous to meet the princess! She wasn't entirely sure what her role as a princess was meant to be quite yet, having just ascended, and she didn't have a lot of confidence that she could be of use to the Empire and Equestria like the other princesses. Twilight was very gentle with Lemon, seeing a bit of herself in her, and offered her guidance whenever Lemon needed it. They became fast friends, though more so with the insistence of Twilight, and when Lemon returned to the Crystal Empire the two often wrote to each other.
There was also a period of time that Lemon was having trouble with her magic, having been born an earth pony, and while Cadence did well with teaching her to fly, she thought Twilight might be better help for magic training. So Lemon actually lived with Twilight in the Canterlot Castle for a time, studying magic from the basics and learning her own particular magic even better.
*
This is a base edit that I did for fun! I just wanted something to do while watching some anime lol plus I'd been eyeing this base for a while with this scene in mind… I've been thinking a lot about Lemon and how she adjusts to being an Alicorn after being an earth pony… because while each pony race has magic of their own, earth pony magic isn't as often discussed or as clearly understood, it's just not as obvious and tangible as unicorn and pegasus magic. So I think giving an earth pony lots of very obvious and powerful magic all at once… it could be overwhelming.