And, if needed
Right-click a syllable;
Select->More->All similar elements;
Open Inspector (F8) and adjust the offset;
Or:
Style/Text-> odd/Even lines->adjust the offset.
Generally speaking, though, you shouldn't need to increase staff distance - MuseScore automatically allocates more space as needed. it might be your lyrics are actually colliding with notes on ledger lines below the staff you are attaching to, in which case you want to increase the "Lyrics top margin" in Style / General / Page. The bottom margin is also useful if you are running into content above the staff below, although this would normally happen less often.
In order for us to provide better assistance, it helps if you attach your score so we can see exactly what to suggest for your particular situation.
Comments
Peruse these sections of the handbook at your pleasure:
Handbook: Layout & Formatting (General Style Page)
https://musescore.org/en/handbook/layout-and-formatting#style-edit-gene…
Handbook: Vertical spacers
https://musescore.org/en/handbook/breaks-and-spacers#add-spacer
And, if needed
Right-click a syllable;
Select->More->All similar elements;
Open Inspector (F8) and adjust the offset;
Or:
Style/Text-> odd/Even lines->adjust the offset.
Generally speaking, though, you shouldn't need to increase staff distance - MuseScore automatically allocates more space as needed. it might be your lyrics are actually colliding with notes on ledger lines below the staff you are attaching to, in which case you want to increase the "Lyrics top margin" in Style / General / Page. The bottom margin is also useful if you are running into content above the staff below, although this would normally happen less often.
In order for us to provide better assistance, it helps if you attach your score so we can see exactly what to suggest for your particular situation.