It depends on your business type and location. Google requires background checks for some LSA categories, but not every business needs one. The requirements can also vary by country and state.
If your category requires a background check, Google may require checks for business owners or certain employees before the business can run Local Services Ads. You may also need to complete other verification steps, such as providing licenses or proof of insurance.
The easiest way to know what applies to you is to check the verification requirements for your specific business category and location before launching your LSA account.