Modern invented blend, possibly from French 'dormir' (to sleep) and Lee.
Dormilee appears to be a modern invented blend, possibly influenced by the French dormir, meaning to sleep, together with the Lee ending common in English-language naming. Even if the exact path is uncertain, the name has a soft, restful quality built into its sound.
Dormilee feels like a name from the era of inventive feminine combinations, where familiar syllables were shaped into something gentle and distinctive. Its effect is mild and dreamy rather than forceful. The name has a quiet, intimate character, and that makes it stand out among more overtly ornate modern coinages.