Modern LCDs work, at least on the lowest levels, like a DRAM. The subpixels which hold the liquid crystal hold charge just like a DRAM cell does. The charge in the cell also leaks and thus has to be refreshed. The LCD has rows (=gate drivers) and column (=source drivers) drivers. The rows are driven by gate drivers to open a row to the column drivers. The column drivers drive an analog voltage to the columns to achieve various levels of polarization through the liquid crystal and thus prevent or allow certain amount of the backlight to reach the user. Color LCDs place color filters in front of the cells to achieve RGB (thus you need 3x the amount of horizontal cells). Monochrome LCDs do not have any filters.
That being said, on the rudimentary level, the LCD is still driven very similarly to a CRT. Gate drivers open each row one at a time, usually in a top-to-bottom fashion. Once a row is open, source drivers, which are DACs with many outputs, drive analog voltages to each of the opened cells of the row. Once that is done, the row is closed, and next row is opened. Often, the source drivers are fed with digital values serially and they are being shifted through each of the source drivers in a daisy-chain fashion as each of the source drivers (=DAC) has only a limited number of outputs and multiple source drivers are usually required to drive all of the columns of the LCD. Therefore, the cells are driven with the desired analog voltage from one side to another, usually left to right. This top-to-bottom, left-to-right raster scan fashion of setting of desired pixel values is very similar to a CRT.
Since the LCD is like a DRAM, there was a push in the past to have a directly addressable LCD. With this LCD, we can draw the full image initially and then only redraw a portion which needs redrawing, saving bandwidth and power. As far as I know, these were only proof-of-concept ideas and never made it to the production and to the commercial world.
This explanation only explains how a liquid crystal display glass is driven. It ignores the fact that a TV or a monitor might have a full or partial frame buffer to aid in scaling, de-interlacing, etc. Either way, the LCD can be driven by simply observing the edges of DE, without any syncs as there are no ramp generators driven by those syncs to aim the electron gun as it was in the era of CRT.
DVI 1.0 specification mentions this fact when requiring HSYNC and VSYNC in 2.2.10: "It is expected that digital CRT monitors will become available to connect to the DVI interface. To ensure display independence, the digital host is required to separately encode HSync and VSync in the T.M.D.S. channel."
That being said, I would like to continue the discussion about all of your experiences with various sources and sinks.