Is there a way in LilyPond to space the score notes evenly?
In the sample image made with LilyPond 2.22.01 the notes are not equally spaced.
The idea is to get all the notes to be spaced equally regardless of their note value.
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\override Score.SpacingSpanner.strict-note-spacing = ##t
You might think that this will make the music easier to read, as the notes will be on some evenly spaced (invisible) time grid. And that might be true is some cases, but it usually is a waste of horizontal space. Besides, the time information is already represented by the note symbols (beams, dots, etc.).
After reading your comments, what you want is the notes to be be evenly spaced regardless of their note values.
In this case what you want to set, is the shortest duration to get a unit space:
\override Score.SpacingSpanner.shortest-duration-space = #16
This also provides a score that is harder to read than the default spacing provided by LilyPond's typesetting algorithm. This complicated algorithm is one of the reasons that makes it such a good engraving program.