I would suspect the gamma voltages if the lines moved around depending on the image displayed - you can use gradient test patterns to determine this.
If the lines stay in the same place, it's probably localised to the column/row drivers.
You are probably right.
But I am still pretty certain it is an analogue voltage problem:
For all who do not know how a TFT LCD works a short explanation:
The source driver generates a voltage according to the desired brightness of the pixel. This is done in parallel for all subpixels in each row. Yes, there are virtually 5760 DACs inside the source drivers!
This analogue voltage is stored into a tiny capacitor in each pixel. The row is selected by N channel FETs driven by the row drivers. The image data is fed into the source pin (therefore they are called source driver). When there is a positive voltage on the gate, this voltage charges the capacitor. A negative voltage is applied to all other rows to hold the value in the capacitor. All 1080 lines are written this way in each frame.
Since a LCD gets destroyed by a DC signal, the voltage generated by the source drivers is inverted in each frame. The liquid crystals are beeing effected only by the absolute value of the voltage.
A possible explanation for the visible effect:
If the negative gate voltage is missing, a high enough negative voltage on the source pin might switch the fets on and the source voltage leaks into each pixel on the same column. Since this only happens for the negative polarity, a DC offset is created. This leads to image sticking and will eventually damage the LCD when applied for a long time.