It seems like:
Lucas wanted to make room for a prequel trilogy, probably about Anakin
Contrary to the common rumor/fan theory/questionable assertion from Lucas himself, the history strongly suggests that Star Wars was originally conceived as a single movie, with maybe an option for a low-budget sequel. (Note that Star Wars was released before movies were expected to have sequels, and sequels were rare. One could argue it was actually Star Wars that initiated the popularity of movie sequels and franchises.)
Then, during the writing of the big-budget sequel that was made possible by the commercial success of Star Wars, Lucas came up with the idea that Vader would turn out to be Luke's father, and around the same time changed the newly-conceived episode numbers for Star Wars and Empire from I and II to IV and V, respectively.
The correlation between the idea and the numbering change strongly suggests that Lucas wanted to tell the story of how Luke's father became Darth Vader, and wanted to leave episode numbers available for a trilogy to tell that story. Assuming this is true, it makes some of Lucas' statements about how he wanted to tell the story mostly true, with the only exception being that he clearly didn't always want to tell the story this way.
See this excerpt from the Wikipedia entry for The Empire Strikes Back:
[Original writer Leigh] Brackett finished her first draft [of The Empire Strikes Back] in early 1978; Lucas has said he was disappointed with it, but before he could discuss it with her, she died of cancer. With no writer available, Lucas had to write his next draft himself. It was this draft in which Lucas first made use of the "Episode" numbering for the films; Empire Strikes Back was listed as Episode II. ... He made use of a new plot twist: Darth Vader claims to be Luke's father. ...
This new story point of Darth Vader being Luke's father had drastic effects on the series. ... After writing the second and third drafts of Empire Strikes Back in which the point was introduced, Lucas reviewed the new backstory he had created: Anakin Skywalker was Ben Kenobi's brilliant student and had a child named Luke, but was swayed to the dark side by The Emperor (who was really a Sith Lord and not simply just a politician). Anakin battled Ben Kenobi on the site of a volcano and was wounded, but then resurrected as Darth Vader. Meanwhile, Kenobi hid Luke on Tatooine while the Republic became the Empire and Vader systematically hunted down the Jedi.
With this new backstory in place, Lucas decided that the series would be a trilogy, changing Empire Strikes Back from Episode II to Episode V in the next draft.
Inspired by the answer here: https://scifi.stackexchange.com/questions/872/why-did-lucas-begin-the-episode-numbering-at-iv