Does this chair come with a left hand tray?

No wiring diagram exists

https://www.google.com/search?q=tranquil+ease+7501+remote+wiring+diagram

You could contact them direct and ask.

Do not attempt to repair your massage chair yourself if a malfunction occurs. Contact Raffel Comfort Sciences For additional questions, please call our customer service representative at 800.307.1058
RAFFEL COMFORT SCIENCES LLC ~ N19W6723 COMMERCE COURT ~ CEDARBURG, WISCONSIN
PHONE: 800.307.1058 ~
FAX 262.375.6037 ~
WWW TRANQUILEASE.COM

But you can get a new remote.

Tranquil Ease 7051 SW3 Lift Chair Hand Control with Heat ...

https://www.amazon.ca > Tranquil-Ease-Chair-Control-...
Tranquil Ease Heat and Massage Hand Control. Model: 7051 SW3. **NOTE** This hand control has an inline harness and does NOT plug into a junction box.**.
Rating: 5 · ‎7 reviews · ‎$84.00 · ‎In stock

you have a couple of options
contact the manufacturer if the chair for a replacement ray
cruise around second hand shops for a cheap chair to get the tray from
go to a cabinet makers and have a suitable tray made up
or if a metal tray go to a sheet metal shop to make a tray
and lastly find a shop that makes fiber glass items and have them make up a tray
any thing you decide will probably cost more that the chair is worth but prices will be what you decide on

left hand wheel motor.. ?might be wheel bearings
springs on each side of chair

Jazzy Electric Wheelchairs Carries Parts for Power Chairs

I don't know about that particular brand name.... but, I bought my two chairs like this from Costco....

Your version has a Dynamic Controls model controller and joystick.
Unplug the charger and engage the motor/brake lever so the chair is no longer in free-wheel mode (con't push by hand)
Turn the chair off, wait 5 seconds, turn the chair back.
If chair still does not run and your wrench is flashing you have a problem. Count the wrench flashes - the flash count indicates the error detected. 3, 4, 5, and 6 flashes indicate and error with the motors.
3=Left motor fault
4=Right motor fault
5=Left brake fault (may not be engaged)
6=Right brake fault (may not be engaged)
Any other fault code usually means the electronics or wiring is bad and not worth fixing.

You can purchase outdoor rocking chairs at stores like Lowes, Target, and Walmart, Home Depot and other home furniture stores. Online, you can find outdoor rocking chairs at the following websites: http://www.amazon.com/s/ref=nb_sb_noss?url=node%3D3742471&field-keywords=outdoor+rocking+chairs&rh=n%3A3742471%2Ck%3Aoutdoor+rocking+chairs, http://www.wayfair.com/Patio-Rocking-Chairs-C416230.html, and http://www.plowhearth.com/outdoor-rockers-and-gliders/category_s2004_d3059_c1094_all.html.

www.overstock.com

The easiest way to do this is to tip the chair forward so that the top of the chair and the arms are on the floor. The weight of the chair will be off the lift frame in this position. Look at the motor and you will see it connected to the frame with 2 hitch pins.
It is easiest to remove the top hitch pin which will now be on the bottom because the chair is upside down. Pull the clip (looks like half of a paper clip) from the pin that goes through the square chair frame and motor round tube. Pull out the pin by lifting the bottom of the motor slightly(now at the top because the chair is upside down)with your left hand and pulling the pin out with your right hand. Find the two nylon washers that have fallen out when you do this.
Swing the motor tube out of the way toward the front of the chair. Hold on to the pin, clip, and 2 nylon washers for re-assembly. Hope this helps.

go and chek the mainual of the chair