If runners are a worry, you can always put them in a container!
I put mine in these “plantainers” that you can find at most big box stores, and they seem to like it: https://www.homedepot.com/p/MacCourt-20-Gal-Large-Plantainer-Preformed-Pond-Liner-PP2615/308771723. Drill holes, optionally paint white (if you live somewhere hot), add soil/fert/plant, and you’re off to the races.
Make sure you know about the University of Arkansas cultivars before pulling the trigger though! They’ve got some pretty impressive varieties, including ones that produce fruit on first-year branches.
Yup - definitely not lemon balm, and sure looks like lemon basil.