I have the same programmer, and I have some of the same chips.
I can tell you with a fair degree of confidence that any programmer you can get, even OLD (80s) that's under $200-$300 on eBay, can NOT program PALCE devices. Those are electrically erasable and to this day AMD and Lattice NEVER published the programming / erase algorithm. It's a closely guarded secret only shared with their NDA signed business partners (like XL-tech or BK Precision).
I am annoyed as you are, because I thought a generic GAL/PAL programmer could do it, but come to find out after eagerly pulling and collecting the chips out of old telco gear, unless I'm also willing to setup a DOS computer with 8-bit ISA card (dedicated to the programmer) and spend a few hundred dollars on the used programmer that might not even work...
Honestly, you're better off buying some of the cheap GAL22V10s still in production by Atmel/Microchip because the TL-866 II+ DOES work with those. And heck, the parts are only a dollar or two each.