I had a similar P0353 error and also experienced a rough engine at various speeds. Mine is a 2007 RX350. The issue was an ignition coil in the middle-rear bank of cylinders. This area is VERY hard to get at and several threads helped me complete the job. You have to remove the intake manifold to get to the rear bank of coils. Once that is done, replacing the coil takes about 2 minutes. The worst part of the job was removing the left (from from of vehicle) rear bracket bolt that holds the back of the manifold. Who ever put this bolt in place ???? UGH. The key to removing it ... and getting room to remove it ... is to remove the wiper assembly and front cowl tray. That adds another hour to the job, but allowed enough room to get to that dreaded bolt. By the way, I never replaced that bolt when I put things back together, as it does not really seem to add much of anything to the manifold, which is held tight with 6 main bolts. Anyway, the job is done, computer reset and I hope this fixes the issues.