The buttons for garage will not program in my Lexus RX 330 2004

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In link below it was said he manually had to close by pulling down and then up a little and then down and the back up a little. The hatch was eventually closed, and it reset(read it in below link.
Lexus RX 350 Questions - The hatchback door will not close using the button on the door and it ... - CarGurus

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Back door - Opening, closing and locking the doors - Before driving - Lexus RX 450H User Manual - Lexus RX - Lexus manuals (lexomans.com)

You probably need to program the garage door opener,not the car.I have only had to program the Craftsman opener in my garage once(our 2005 Grand Caravan has a built in opener)The opener should have a programming button(my Craftsman opener's button is under one of the light covers).It will probably have the programming instructions near the button(in TINY print).You will want to have ALL of your garage remotes handy(to make sure they all still work after adding the car's remote-some openers have a maximum number of transmitters allowed.

You should see three buttons on the driver sun shade. Let's name them from left to right 1,2, and 3. Start by clearing any old codes. To clear codes press buttons 1 and 3 simultaneously until the light starts blinking. Release the buttons simultaneously. Before starting to program the car remotes you must have your gate hand held remote ready with a good charged battery. Now, to program your first gate car remote let's choose button 1. Press button 1 until it start blinking (about 20 seconds). Keeping button 1 pressed, activate your hand held remote close (about an inch) from the car button 1, until the light blinks faster than before. Release both remotes simultaneously. You are done programming your car remote button 1. For two additional gates remote controls programming repeat the procedure with button 2 and then with button 3.

If this is the 3 button HomeLink Transmitter usually centered overhead above the rear-view mirror, this should work:

While the engine is turned off follow these steps to program up to three channels:
1. Decide which one of the 3 channels (one of the 3 HomeLink buttons) you want to program.
2. Press & hold the desired button through step 3.
3. When the HomeLink indicator light begins to blink slowly(this may take up to 30 seconds), hold your hand-held garage door remote about 1 to 3 inches away from the buttons & then press and hold the button on your garage door remote. Continue to hold both buttons until the indicator light on the HomeLink begins to flash rapidly(this may take up to 90 seconds).

If it still doesn't work, make sure the batteries in your garage remote are not weak, and try again moving the remote back & forth and left & right or turning it upside down while programming.

Also note HomeLink will not work with older garage door openers, especially not with ones manufactured before April 1st 1982.

Make sure you have a fresh battery in the garage remote. Drive away about a block and park. Press the two outer buttons on the IS for about 20 seconds , they will flash 10-15 seconds and then go out,erasing any old codes in the car.
Then select a button position, 1-2-or3 on the car for your garage function. Hold your garage remote to the car's button pad and depress the garage remote button and the cars button (1-2 or3)continually. The LED in the cars touch pad will flash slow, then fast then go out. Once these steps are completed the car and your hand held are syncronized...thh car has recieved the remote function. That is step 1 for all vehicles.

Now you need to return to the garage and "introduce" your car to the garage door opener's receiver. Depending on the brand there will be a "learn" button on the garage door opener. You will climb a ladder and push the learn button as per instructions in the opener manual or on the stickers on the opener motor itself, if it is a Chamberlain, Liftmaster or Craftsman....
These buttons will be pressed to erase old opener codes or program to add new devices...which is what your car is.
Each opener has its own series of functions but generally after initial set up of the ceiling unit, you will depress the learn button and hold for several seconds. Then within 30 seconds , you will depress the cars button for about 2 seconds and release, the lights will flash on the ceiling unit in the garage indicating success and the next time you press the cars button the system works.
For complete detailed instructions go to the HOMELINK web site. It covers most cars by model and openers by brand with VERY detailed instructions.
Nice car! Enjoy and post back with results

GOTO HOMELINK.COM

THEY MAKE THE SYSTEM AND HAVE INSTRUCTIONS YOU CAN DOWNLOAD.

PLEASE NOTE: NOT ALL BRANDS/MODELS OF OPENER WILL WORK WITH THIS SYSTEM.

HOPE THIS HELPS

There are 3 programmable Homelink buttons you can use for different remotes. Just to the right of the buttons there is an indicator light.

Decide which button you want to program. Point the none battery end of your remote 1"-3" away from the Homelink panel and press both the remote and desired Homelink button down and hold them down at the same time. After about 20 seconds, the Homelink indicator light will change from a slow flashing to a rapid flashing. You can then release both buttons,
If the garage door responds to the Homelink, your done! If not, your garage door uses a rolling codes transmitter and must be trained.
Find the training button on your garage door opener's transmitter (usually mounted on the ceiling). Press the training button and within 30 seconds press and release the programmed Homelink button twice. If the garage door opener operates, you're done! If not, press and release the Homelink button a third time and the garage door should respond. If it still does not, you may have a very old garage door opener with a none digital transmitter (like I did). In that case, you either need to buy a new opener or try to replace the transmitter with a modern digital unit (as I did). Advantage: cheaper than a whole new garage door opener.
Disadvantage: The newer openers incorporate safety features that my old opener does not have.

THE DEALER PROGRAM THE REMOTE OR DOWNLODE THE AUTO MANUAL.
BOOKS4CARS.COM

I purchased a Chamberlain belt garage door opener. It was great! The lease on my duplex ended and the landlord bought it from me.

I found that the best way to program my vehicle's HomeLink buttons (to read the remote) was to do the learning procedure in a parking garage. This way the signal is not interrupted by all the waves around us.

Check out the Homelink Website. I found instructions for my wife's GS300 there. I haven't tried it yet, so I'm not 100% sure this will work.