Tightening a loose bottom bracket I bought a new bike a couple of months ago. Recently I noticed that the bottom bracket is getting loose. It is regularly unscrewing itself, and while I can screw it back in partially manually, I cannot generate enough torque to get in back in there all the way in. What tool should I use to do this? I have found some 8-notch bottom bracket tools, but they would require removing the cranks, and I'm not sure that they're the correct thing anyway.
It looks like what you have is a cartridge bottom bracket with a left hand cup with both Octalink style 8 notches (even though the axle is clearly square taper) and the more common 20 splines

Park tool BBT-18 (Octalink), BBT-22/32 (splines) with work, as will the dual purpose Lezyne tool you linked to.

Yes, you will have to remove the crank to properly tighten the cup. You probably want to do the drive side as well. To get the cranks off you need a crank puller (such as Park CWP-7). To tighten the bottom bracket and re-install the cranks you need a fairly hefty torque wrench as it's critical the cups and crank bolts are tightened to the correct torque.

For infrequent jobs where special tools are needed it's often easier to have a good local bike repair shop do the work.