Lilting Lullaby

Yes. Countering your spell clears it from the chain, so it is an illegal target when Lilting Lullaby resolves.^{426.1.a355.9.a.2359.3.e.2} Lilting Lullaby still resolves, but its counter instruction is ignored because the target is illegal.^{359.3.e.1359.3.e.5359.3.e.6} The spell-play restriction is linked to that ignored instruction through "its controller," so the restriction is also ignored.^{359.3.e.14359.3.e.14.a}