Can I remove a buff on my turn? For example, I'm playing Lee Sin Blind Monk. I have a unit buff. I remove it, then I use the buff from the legend and use Mistfall to ready it again?

No, you cannot voluntarily remove a buff from a unit without a card effect. There is no basic game action to just "take off" a buff (Rule 702.2). Buffs can only be spent when a card or ability tells you to — like Wallop ("as you play this, you may spend a buff as an additional cost"), Monastery of Hirana (spend to draw), or a "Spend my buff:" activated ability on a unit.

However, if you have a card that lets you spend that buff, the rest of your plan works. The sequence would be:

1. Spend the buff via a card effect (e.g., Wallop targeting the buffed unit — the buff is spent as an additional cost).
2. The unit now has no buff.
3. Activate Lee Sin Blind Monk's legend ability (1 energy, exhaust) to buff that unit — this succeeds because the "buff slot" is open (Rule 702.3.a).
4. Mistfall triggers: "When you buff a friendly unit, you may pay Body rune and exhaust this to ready it." Pay the cost, and the unit readies.

You just need a card that gives you a reason to spend that buff in the first place. Without one, the buff stays put.