\markup "lyrics here seem to be a bit too far from the staff..."
{
    \repeat unfold 16 { a'16 }
}
\addlyrics { \repeat unfold 16 { run } }

\markup \wordwrap { ...especially compared to this example.  Notice that the actual distance between staffsymbol and lyricText is identical in both cases: }
{
    \repeat unfold 16 { b'16 }
}
\addlyrics { \repeat unfold 16 { run } }

\markup "increasing padding and decreasing basic-distance is a bad idea because it will break this case:"
{
    \repeat unfold 16 { a'16 } b4
} 
\addlyrics { \repeat unfold 17 { run } }
\markup "Lyrics are already quite far from the staff here because of a quarter b note; they shouldn't be lowered more."