It's totally possible to live on a retail lot, but I don't believe it's possible to use a residential lot as a retail location (you won't get customers). As Oshizu said, you will still need to own a residential lot in order to purchase a retail lot and begin your build. You can have a separate place in the retail area that is used as a living area, you just want to make sure you lock the doors so only household members can access those areas.
One major problem I've encountered with this method was when I tried to live at my restaurant. If you have a table and chairs inside the residential area of your retail lot, you may get bugged hosts that keep trying to seat customers at your personal table, but can't get through the locked door. It's pretty obnoxious. The good news here is that if you're just planning on running a retail location and not a restaurant, you shouldn't have the same issue.
Best of luck!