Why do I sometimes get a speed boost when leaving the spawn area?
Solution 1:
Lúcio was nearby.
One of his skills, Crossfade allows for nearby team members to move faster than usual.
Lúcio continuously energizes himself—and nearby teammates—with music. He can switch between two songs: one amplifies movement speed, while the other regenerates health.
Emphasis mine.
As for why the speed increase varies, it's because of another one of his skills, Amp It Up, which boosts the effect of his Crossfade songs.
Lúcio increases the volume on his speakers, boosting the effects of his songs.