"Ná hith a dinnéar."
Translation:Do not eat her dinner.
"his dinner" is a dhinnéar.
"his" causes lenition, where possible, "their" causes eclipsis - a ndinnéar, and "her" doesn't cause any mutation. When the first letter of the noun can't be lenited or eclipsed, you don't have any indication of whether a means "his", "her" or "their" - for example a leabhar.
The latter would work, but it would be spelled hithigí rather than hithígí.
Theres no subject in the translation but do the different verb forms still imply whos being told the command?