CAn I react to Lilia's Legend ability activation of her legend ability

Yes. Lillia's Legend (Bashful Bloom) has an activated ability ([4], [T]: Play a ready 3 [M] Sprite token with [Temporary]), and activated abilities always go on the Chain, creating a Closed State.

That means after she pays the cost and activates it, the ability sits on the Chain as a Pending item, and you get a window to respond with Reaction spells or other effects before it resolves (Rule 377.3). This is true for any legend with an activated or triggered ability — the only legend effects you can't react to are replacement effects (they don't use the Chain).

One note: responding doesn't stop her from paying the cost — the token just won't be played until the ability resolves (assuming you don't counter it).