Hi Night Vision,
I'm a noob also and have a similar scope, but I'm not exactly sure what the difference is with the OTA between the LX90 classic & LX90GPS. I only have a 26mm eyepiece at the moment which gives a magnification of approx 77x and I also experience some image shift when I focus but I don't lose the image as you do, maybe with a 15mm eyepiece at 133x it may react the same.
A suggestion given to me to lower the amount of image shift was by running the focus mechanism to its full travel about 20 times in order to re-distribute the grease supporting the mirror "slew" on the central baffle tube. So far I ran the focus mech twice as I counted about 90 twists with my wrist each full travel and had to have a rest besause it hurt
, so I plan to try this over the next few nights to see if it helps.