No. Because the door, if it is a flush door, won't be solid wood.
Interior fire doors (i.e. heavier flush doors) consist of a dense chipboard core around which, typically, a softwood lipping is glued on all 4 sides. This lipping varies but is often in the region of 10 to 20mm thick. The faces are often thin glue bonded plywood with a show grade veneer outermost, in a species such as mahogany, lauan, meranti, etc. Finally the long edges are lipped eith 6 to 10mm thick hardwood. There are variations on this such as the hardwood plywood being applied after the edge lipping oo rge lipping being round 3 or even 4 sides of the door, but the fundamental issue is that the core is chipboard, not solid wood.
Lightwood doors are even filmsier, with a cardboard "egg carton" core, so they are even worse to deal with if you cut them. To make matters worse they have denser hinge blocks (generally a block of chipboard or softwood) glued on the inside on only one side with a lock block of the same material on the middle of the rail on the opposite edge which makes them very awkward to modify
A competent, experienced carpenter can often make a passable job of cutting and re-lipping a solid core fire door on site, but the technique does vary according to the door specifics and it is easier to be successful if you have a rail saw, guide rails, a vacuum, an 18 ga pinner and a router