Cut the top, bottom, and skin off of the grapefruit and then slice your knife right next to each segment to remove them, leaving you with just the flesh wedges (see picture).
Cut the grapefruit wedges that you have removed into chunks (a little larger than you want, as they will break some with mixing) and place in a small bowl. Squeeze the "guts" (leftover white membrane from the grapefruit) of one grapefruit into the small bowl to get some of the liquid.
Add the finely diced red onion, basil, juice of 1/2 lemon, and the olive oil to the grapefruit. Stir gently to combine. Season to taste with salt and pepper. If too tart, add a little sugar as desired.
Chill until ready to serve. Serve as a dip or use on top of proteins.
Notes
I try to remove as much of the white part of the grapefruit as possible because it can be bitter, but a little here and there is fine.Mint is a great substitute for the basil, and orange is a great substitute for the grapefruit.