A lever handle is easier to grip than a round knob for many hands, and swapping one is often within reach of a household with basic tools. The question is not whether the new handle fits in your hand. It is whether the door and latch will take the new hardware without changing how the door closes.
Local option: New Plan Care gives families in the St. Louis area in-home help so a parent can stay home: companionship, help with bathing and dressing, meals, and overnight care. Call (314) 405-0887.
Check what the door already tells you
Open and close the door several times with your own hand. Notice whether it sticks, sags, or rubs on the frame, and whether the latch catches cleanly. A door that already fights the frame will not be fixed by new hardware, and a carpenter should look at it first.
Match the parts before you start
Measure the backset, which is the distance from the edge of the door to the center of the hole, and check the hole diameter in the door face. Most lever sets are sold for standard sizes, but older doors can differ. Compare the measurements to the packaging before you remove anything.
What a household can usually do
If the holes line up, the latch sits square, and the door closes well, the swap is often a matter of removing the screws on the old set, pulling the latch and strike plate, installing the new parts, and testing the latch several times. Tighten screws by hand first so nothing strips.
When to hire it out
Call a carpenter or a door installer if the holes do not match, the latch is out of line, the door is heavy or rubs the jamb, the old hardware is painted over and will not come out cleanly, or the set needs an opening mechanism that does not match the rest of the room.
The bathroom check
Any lock on a bathroom door should be one that someone outside can open in an emergency. Before you choose a lever set for a bathroom, confirm how the outside release works and test it. This is a safety decision for the family to settle with the installer, not a detail to leave until after the install.
If you want to see who in your area does this kind of work, the local help page lists where to start.