No, you don't have to even though you are highly encouraged to do so. You can make a will without a lawyer as long as the requirements of a valid will are satisfied.
In Singapore, these are the requirements for a valid will:
1. It must be in writing;
2. Testator (the person who is writing the will) must be at least 21 years old;
3. Testator must sign at foot of the will in front of at least 2 witnesses;
4. The witnesses cannot be beneficiaries (people who will benefit from the Will) or spouses of the beneficiaries.
Additionally, the testator must be of sound mind (have mental capacity) and not under undue influence (made the decisions voluntarily) at the time the will was written and signed.
Read more: Guide To Making a Will - Singapore Edition