While there is no requirement to use a lawyer, probate is a rather formal procedure. One minor omission, one failure to send Great Aunt Tillie a copy of the petition, or a missed deadline, can cause everything to come to a grinding halt or expose everyone to liability.
The death of a family member or friend sometimes tends to bring out the very worst in some people. Experience shows that even in close families there is a tendency to get overly emotional about relatively trivial matters at the time of a loved one's death, such as who gets the iron frying pan and who gets the kettle. Such minor matters, or any delays or inconveniences can be upsetting, pose issues of fairness, and create unfounded suspicion among family members. Thus it generally is a very good idea to "let a lawyer do it".