I recently purchased a Lenovo S340 laptop with a 512 SSD and a 2T standard hard drive. I wiped windoze and installed LM 19.2 XFCE. I put EFI on the SSD and also root. I put home and swap on the 2T.

From what I have read SSD drives may not last as long as a mechanical drive. So I am going to install MX linux on the 2T, so in case the SSD fails at some point in the future I will still be able to access MX linux.

My question is if the SSD fails will I still be able to boot MX linux with the EFI partition on the SSD? Or will I need to put a second EFI partition on the 2T drive to boot MX? Can I even do that without creating problems?

Any device can fail - the days of excessively worrying about SSD have long gone. However Lenovo has an appalling history, and is just as likely to require the EFI on the SSD. Simple enough to back it up - it's just a [V]FAT partition.
The firmware will go looking for the EFI - I advise against multiples to avoid the confusion. If it breaks, you can always still boot a liveUSB and chroot into your Linux. Worked that way forever, still works.

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From a usb that has grub, refind, supergrub, or something similar yes. From the 2t drive without an efi partition no.

So to answer you next questions yes you will need an efi partition on the 2t if you want to boot from it when the ssd dies. Yes you can have two efi partitions on the same system. As far as problems with 2 efi partitions hard to say as uefi firmware/bios isn't same on different system, However most problems with this will be annoyances that can be worked around. However as syg00 says can cause confusion

The other possible issue would be getting the linux on the 2t update when the ssd dies, If you never boot into it every so often to keep it up to date.

The other option is to not install a root partition on the 2t, just the home and swap, and when the ssd dies, use a live usb to make room on the 2t for the root partition and do a fresh install then take over the home partition.

If it was me I would put root,home,swap on the ssd and store my data on the 2t, that way if something happens to the root system or the configuration files in the home directory, then can do a reinstall without affecting the important data. As already mentioned if you didn't want to replace the ssd when it dies, then from live usb make room on 2t to do a fresh install.

Who knows, your 2t may die before the ssd.

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I want to thank both you guys for the quick and pertinent response! I'm just tinkering at present so I think I will put another EFI partition on the 2T and see what happens. I am curious to see if grub will pick up both operating systems or just one, and which. When I do I'll post and let you know how it worked out for me. When I do install the 2nd os I will be using them both off and on, one at a time, so they will both be updated.

Here is another question you may have thoughts on: I have another laptop with three linux os installed. Can I share a swap partition between 2 of them without problems as long as only 1 os is running at a time?

Yes you can, but you need to be careful/aware. As normally installed each install will typically mkswap on any swap partition it finds. Also typically, mainline distros insist on using UUID in fstab, so all the other systems fail on boot. If you change the UUID to device nomenclature (/dev/sda3, whatever) everywhere it works fine.
However - don't go hibernating and expect things to work if you boot back to a different distro. Common sense, but often ignored.

I only run one swap on all my multi-boot systems.

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What you could do is what I would do: Partition the 2T in advance as if I was going to use it only, but actually use only the data partition, until such time as the SSD did die, at which time if it ever came I would install an OS configured to use the VFAT as the ESP. The immediate extra VFAT wouldn't be an ESP until such time as it was actually configured as such. The unused partitions need take up less than 5% of the 2T, so you wouldn't likely miss the space, and if you did, you could replace it with something larger.

I say would because it differs little from what I am doing. I have 5 different Linux operating systems on this PC's 120G SSD, and partitions on two 1T HDs comprising RAID1 devices for various types of data. If my SSD goes, I take it out, plop in a backup clone, and continue normally as if no failure had occurred.

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Well, when I installed MX on the 2T drive, the installer did not give me a choice of which EFI partition to install boot files to. It only showed the EFI partition on the SSD. I may fool around with it a bit more if I have time, but I think I will mark this thread solved for now. I want to thank everyone for their excellent advice and time!