This goes deeper than you think. We noticed this a couple of days ago and it was going to be included in a larger post, but basically at the moment Lilys not only get consumed, but the CD reduction effect actually works on anything that consumes it. For your example with Muse, your cool down on Muse was actually reduced as any of your normal CD's would have been by your Lilys consumed. This is likely a bug.

Safeguard CD w/ 3 Lilys: 36s
Muse CD w/ 3 Lilys: 36s
Bolt CD w/ 3 Lilys: 18s
etc.