A single tie may be engraved manually by changing the staff-position property (an offset) of the Tie grob; if there are multiple ties at the same musical moment, they can be adjusted manually by changing the tie-configuration property (a list of offset/direction pairs) of the TieColumn object.
The offset indicates the distance from the center of the staff in half staff spaces, the direction can be either 1 (up) or -1 (down).
Note that LilyPond makes a distinction between exact and inexact values for the offset. If using an exact value (i.e., either an integer or a fraction like (/ 4 5)), the value serves as a rough vertical position that gets further tuned by LilyPond to make the tie avoid staff lines. If using an inexact value like a floating point number, it is taken as the precise vertical position without further adjustments.