Downloaded the Ubuntu 16.04.2 .iso
install disk and flashed it onto a USB stick.
Booting on the USB stick, there is no memtest86+ option (along with "Try Ubuntu").
Is there a way to add it to the install options?
(it's for a UEFI boot PC running normally Windows, its owner does not want to install Ubuntu. "memtest86+" is completely free (unlike "memtest86"), but is quite old, and does not offer a UEFI boot - this is why having it within the Ubuntu options makes things easier)
Memtest86+ does not work in UEFI mode
Memtest86+ does not work in UEFI mode because it is a 16-bit program. But if you can boot the computer in BIOS (CSM, legacy) mode, it works.
See: Where is the memtest option on the Ubuntu 64-bit live CD?.
Memtest86 works in UEFI mode
There is another version, the 'original' but now not FOSS version memtest86, and it works in UEFI mode. There is a commercial version and a free version (no cost, but not open source code).
See: www.memtest86.com/download.htm.
Adding newest freeware memtest86 to UEFI Grub2
Here is a great tutorial on how to add the freeware memtest86 to UEFI Grub2. It's especially useful if you are working on a remote machine, and inserting a physical usb is out of the question.
See this Ubuntu oriented tutorial.
See this example of doing this on a remote server, but based on the above tutorial.
No.
Best alternative: create a live boot memtest usb/dvd. You can create it from Linux, Mac or Windows (basically they provide an installer for all three but the software itself is identical).
For UEFI you need the MemTest86 v7 Free Edition version (link below downloads that one). Instructions for the USB version (there is also a DVD version and a floppy disk version at the links above):
Pretty generic.
According to this discussion it can't run in UEFI mode because it's a 16-bit program.
If available, booting the live USB (or DVD) in Legacy/CSM (AKA "BIOS mode") should bring the memtest86+ option you want to the live menu.
Memtest86 works in UEFI mode. It has a free variant but is not open-souce.
Download the iso from https://www.memtest86.com/tech_booting-cd-dvd.html
Burn it to usb drive (I used etcher).
Now restart your machine and boot from the usb drive.
P.S.
Diagnosing RAM with tools most of the time do not work. I ran Memtest86 for 5/6 hours. It reported that the RAMs do not have any issues. Then I took out the RAMs i doubted and the system started running smoothly.
Just keep one RAM and remove others. Then run your machine for a while and check if there is any issue or not (remember, the issues can be very subtle, for example keyboard does not work for 1-5 seconds every once in a while). If there is no issue then it is a good RAM. Then check ram 2,3...n.
Again if you find a faulty RAM, then maybe the RAM is not fault but the slot where it is attached.
Please note that all RAMs and slots can be good but if there is a miss match (bus speed or brand) then it can cause issues. So, you have to make sure that combinations also work. For example, use same brand and same bus speed RAMs together and test the machine for a while (remember, the issues can be very subtle). Then attach another brand / bus speed RAM and test for a while. Then maybe enable XMP and test for a while.
So, hopefully now you understand why it is better to diagnose RAMs physically than with tools.