Lillian Morgan (Exp.1) plays ...It's who you know as shootout action

What happens if, as a shootout action Lillian chooses to play “…It’s who you know” from her discard?

Can she even play it?
I think not because “…It’s who you know” is a noon action.

If she could, would that mean another shootout could happen while her shootout is still in it’s actions phase?

More generally, is it possible to have a shootout within a shootout?

Lillian Morgan
Dude • Draw 1 • Influence 5 • Cost 10 • Upkeep 3
Experienced 1 • Huckster 2
If your outfit is Entrepreneurs, Lillian’s cost is reduced by 1 for each Horse and Ranch you control.

Noon/Shootout: Play an action from your discard pile (as if it were in your hand). After the card resolves, boot a spell on Lillian or ace that action.

…It’s Who You Know
Action • Cost 0
Noon: One of your dudes calls out an opposing dude at their location. All dudes in both posses use their influence rather than their bullet rating for the shootout (but keep their bullet type). Your dude becomes a stud for this shootout.

You are correct. Lillian cannot play this card as a Shootout action, only as a Noon action because it is a Noon action.

There are no Shootouts within a Shootout.