I've dealt with this many times on my 2000 Es300. I can tell you with almost 100% certainty that you have one or more coil-packs that have gone bad. There are six (one for each piston), and when one stops working, you get a cylinder misfire. Your car is shaking because when a cylinder stops firing, it becomes dead weight on the crankshaft, which throws the engine off balance.
The fix is pretty easy... you only need about 10-15 minutes, an allen wrench, and a new coil-pack (about $100 from Lexus). The most difficult part is identifying which cylinder is misfiring. Luckily, the coil packs (which sit above each spark plug) are extremely easy to access from the top of the engine and don't necessitate the removal of multiple parts to access them.