This word is not compatible with the name Lalaith “Laughter” attested in The Silmarillion. The most likely explanation of this name is that it is the unattested verb *lala- “laugh” with the abstract noun suffix -ith seen in tirith “watch(ing)” and sirith “flowing”. This indicates a primitive form ✶lala- instead of ✶glada- (both primitives produce Quenya lala-). If you were to accept gladh- as the Sindarin word for “laugh”, then the word for “laughter” would perhaps be the equivalent abstract noun *gladheth, and the name Lalaith might be a mix of Quenya and Sindarin.