Can my opponent play a reaction spell to my Lilting Lullaby?

Yes. Reaction spells can be played during a Closed State on any player's turn, and your Lilting Lullaby is itself on the chain — so your opponent can add a Reaction spell on top of it (Rule 813.1.c.1).

Two things follow: (1) your opponent can play their Reaction before Lullaby resolves — the "can't play spells" restriction only takes effect once Lullaby finishes resolving; and (2) if that Reaction counters Lilting Lullaby, the restriction never applies at all (Rule 425.1.a). Note that after Lullaby resolves successfully, the restriction does apply — the window is only while it's still on the chain.