Crazy notion of the day: Can this cute little puppy be trained to run in reverse?
To cut to the chase, no. It would be easier to give a precise answer if we had the datasheet for the Portable's LCD, but most of those ancient monochrome LCDs don't use timing anything like a CRT. (This was alluded to in the other thread you linked to this one. Some of these LCDs aren't even all a single plane, they have separate refresh zones for the top and the bottom half of the screen that operate simultaneously, etc.) If you want to try to convert a conventional raster and display it on this thing you're pretty much going to have to capture a full frame at a time on the "in" side and read it out in the LCD's format on the other. Which means your converter is going to require a framebuffer large enough to hold the whole thing, not just a rolling line buffer or other shortcut. Even if it were fast enough to do the capturing part (which would definitely be a stretch) an Arduino's AVR328 has 2K of working RAM, that's not going to cut it.
In principle something leagues more powerful could do it,
the RGB2HDMI pulls a roughly similar feat using a Raspberry Pi Zero with a little bit of help, although it must be said that the Raspberry Pi's output side has significant hardware assist *and* the pixel clocks that the RGB2HDMI can officially handle are all significantly lower than VGA. I don't know if any modern SoC's LCD drivers could be convinced to interface with the Portable's LCD, my gut feeling is "probably not", but a datasheet would help *a lot*.