Can I play Flurry of Blades, opponent counters with Lilting Lullaby. Can I react with another Flurry of Blades in reaction?

Yes, you can react to Lilting Lullaby with another Flurry of Blades.

Both cards have the [Reaction] keyword, which permits them to be played during a Closed State (Rule 813.1.c.1). When your opponent plays Lilting Lullaby to counter your first Flurry of Blades, the chain becomes closed, and you are allowed to add another reaction to the top of it.

The Chain State

1. Bottom: Flurry of Blades (your first copy)
2. Middle: Lilting Lullaby (opponent's counter)
3. Top: Flurry of Blades (your second copy)

Resolution (LIFO - Last-In, First-Out)

According to Rule 327 (Chains) and the LIFO resolution order:

1. Your second Flurry of Blades resolves: It deals 1 damage to all units at battlefields.
2. Lilting Lullaby attempts to resolve: It targets your first Flurry of Blades to counter it. Since that card is still on the chain, it is countered, does nothing, and is cleared from the chain (Rule 425.1.a).
3. Note on Restrictions: Because Lilting Lullaby resolves, its secondary instruction—"Its controller can't play spells this turn"—will apply to you for the remainder of the turn (following the clarification in RiftJudge FAQ #10260).

Important Note on Targeting: As noted in RiftJudge FAQ #9178, Flurry of Blades does not target units. It programmatically selects all units at battlefields. Because it does not target, it does not trigger any [Deflect] costs.

Note: I could not fully verify the [Reaction] keyword status of Flurry of Blades against the retrieved rules.