Note that from my reading of the QXGA Panel data sheet referenced in an earlier post, that display is what is called a "Dual-Link" LVDS. It needs 8-lanes to achieve that resolution. Regardless of the interface, TFT panels themselves will only accept data at their native resolution. Any scaling would have to be done by external circuitry on those adapter boards. Also note that while many of these "everything-in-one" adapter boards which accept VGA/Composite/S-video/DVI/HDMI may look the same as each other, there is still a bit of programming done on the board to adapt it to the target display. Most of these boards I've encountered are based on a conversion chip made by RealTek(The chip with the crab icon on it) which is actually quote sophisticated and also includes the On Screen Display for menus for brightness/contrast/etc. I don't recall off the top of my head whether they have a dual-link LVDS version of that chip.
All older panels that are LVDS or TMDS require dual link to do resolutions higher than 19x10 or 16x12 IIRC. That's why newer standards such as MIPI and Display Port were invented. They use a higher data rate to get more pixels with less data lanes. I was actually surprised to see mention of "Old" machines with QVGA, until I remembered that Dual-Link(Sometimes called Dual-Channel) was a thing...