In general, no HD TV looks good next to a UHD 4K display. It's worth it to upgrade. The only question becomes which one? OLED and LCDs are converging in the absence of a "better" technology, as each matures.
For burn-in, I'd suggest looking at Rting's test.
https://www.rtings.com/tv/learn/real-life-oled-burn-in-test
Conclusions: "...we don't expect most people who watch varied content without static areas to experience burn-in issues with an OLED TV."
Your burn-in concerns may be overblown.
Rtings also has a summary table you can filter to look at all the LG displays they've reviewed, to see which OLED or LCD display better meets your viewing needs.
Have fun,
Frank