Achoring with Drill versus Anchoring with Spanner
First, just a general note - driving lag screws like the one pictured above into concrete or stone would need an anchor drilled and set into the concrete, and you'd also want a washer. If you don't have anchors underneath, you'd probably want a concrete anchor screw or another type of fastener.

That said, you'll likely be able to apply more torque with a spanner than you will with a drill. The drill will make driving it go faster and easier, but if you're concerned with hold, I'd finish with the spanner regardless. Sounds like all you really need is a square-drive socket adapter: