Did you check the fuses in the engine compartment, there is one more fuse for the lights inside of the car.
your 15 A fuse located behind the coin box is blown.
Open the dashboard fuse panel and look for the fuse marked cig ...replace it
It is the same fuse as the cigarette lighter.
I assumed that your clock is not working. On the lower left panel of the dashboard, there is a little tray. Open and pull the tray out. The fuses are in the back. Locate the one for cigarette lighter (sticker on the back of the tray shows the locations of the fuses) and replace that fuse even if it looks intact.
The fuses are located behind the little change cup just above the drivers left knee. You have to remove it to get to the fuses. And there should be a diagram on the back of the little cup.
There is a fuse cabin below the steering wheel on the left. Open it and inside the lid has the details of all fuses. Also check your Owners manual.
In a 2001 Lexus ES 300, the fuse for the clock and cigarette lighter is located in the engine compartment fuse box. Specifically, you should look for the fuse labeled "CIG" or "Cigar Lighter" and check the owner’s manual for the exact position and amperage. If the fuse is blown, replacing it should restore functionality to both the clock and cigarette lighter. Always ensure the vehicle is turned off before checking or replacing fuses.
Check your fuses
The fuse is called the 'Dome' fuse and usuall it's in a block of fuses under a black plastic cover next to the battery.
You need to specify exact model you have (CE, LE, XLE) and type of engine (4 cylinder or V6). In between, the coin compartment you have removed has a sticker on it is back with all required information you need.
Behind the coin holder on the left side of steering wheel.
if the fuse is blown on that circuit you can lose power on those items. before replacing the fuse, make sure that there is nothing in the cigarette lighter socket that could be causing the short and subsequent blown fuse. (its on the same fuse)