please note that \partial or \upbeat, whatever you call it, has
musicologically a special meaning: the first, incomplete bar, and the last
bar of a piece or of a major section of a piece (typically the bar before
the next "||" bar glyph) should sum up to a complete bar.
For example, if a song with 4/4 meter starts with "\partial 4 f4", the
last bar should, by convention, have a total length of 3 quarter notes.
Having said that, you never should use "\partial" or "\upbeat" somewhere
within a piece. If lily nevertheless accepts it within a piece without
issuing an error or warning, I consider this a bug.