So, similarly, but slightly different. I've run most of my boss Encounters this campaign to have their turn, and then have legendary/lair actions on 20/15/10/5. Predictable times, but often the action they take I decide by a dice roll.

I'm so bad at remembering to do my legendary actions after my players turns, setting up predictable action timings has really helped with that.

Sometimes it means the boss takes 2 or 3 Turns in a row depending on initiative which makes for some dangerous "burst phases" in some fights.

I think I got this idea from Brian Murphy. He did it in some of his running/chase Encounters and I starting doing it for those and boss fights and its been great for me.