Reaper is a DAW and although DAWs can approximate the score and even allow you to drop notes into a “score”, scores are 2nd class citizens in a DAW. Unless your midi regions are all perfectly quantized the scores out of a daw are usually unreadable without a lot of fiddling.

When you say “write” music it’s important to clarify what you mean. If you mean composing music then the best bet is to use a notation app such as Dorico or Musescore (the latter being free). These apps allow you to compose music by dragging notes around staffs easily, listen and loop, and support playback via vsts, exporting to various formats and engraving well-formed scores.

Lilypond is not a notation app, it is an engraving app. it is essentially a CAD program that converts ascii symbols into music notation. When you combine it with its user interface, Frescobaldi, it becomes a full fledged engraving app. Although you could compose in Frescobaldi as you engrave, it would be very cumbersome. there are too many advantages to the notation apps.

The notation apps do engraving, and do it well.