Fernand Lemaire's Berceuse is a straightforward, melodic piece that adheres to the established conventions of the genre. It is noteworthy for its clear, transparent structure and light harmonic ornamentation.
Focus on evenness of touch within the arpeggiated accompaniment figures.
Comparable difficulty and character — good candidates for what to learn next.
Berceuse is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 5.
You should be comfortable at Henle level 3 — meaning you can already play level 2–3 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of Berceuse lasts about 3 minutes.
Berceuse is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include Blau Veilchen by Richard Eilenberg, Berceuse by Léon Boëllmann, Berceuse by A. Simon — see the full similar-pieces list on this page.