Lay Low vs Genina, The Red Poet

Dear all,

If Genina is Anarch, can she play Lay Low before activating her own ability that would send her to torpor so she could not play Lay Low afterwards?

Card Texts:
Name: Genina, The Red Poet
Cardtype: Vampire
Independent. Red List: If a blood hunt is successfully called on Genina, she goes to torpor instead of being burned.

Name: Lay Low
Cardtype: Action Modifier/Combat
Requires an anarch.
Only usable when a blood hunt referendum passes and would burn this anarch. Move this anarch to the uncontrolled region (breaking any temporary control effects). Any cards and counters on this vampire remain with him or her (but are out of play as long as the vampire remains uncontrolled).

Thanks in advance,
Rémi.

It seems both effects take place in the same time window, and without priority declared, meaning you can choose the order. In other words, I'd say yes.