By default, LilyPond does not allow the same articulation (e.g., an accent, a fermata, a flageolet, etc.) to be displayed above and below a note. For example, c4_\fermata^\fermata only shows a fermata below. The fermata above gets simply ignored.
However, one can stick scripts (just like fingerings) inside a chord, which means it is possible to have as
many articulations as desired. This approach has the advantage that it ignores the stem and positions the articulation relative to the note head. This can be seen in the case of the flageolets in the snippet. To mimic the behaviour of scripts outside a chord, 'add-stem-support would be required.
The solution is thus to write the note as a chord and add the articulations inside of <...>, using the direction modifiers ^ and _ as appropriate.