Hello again
There is a ST7920 controller, which is HD44780 compatible, so LCDOUT can be used to display not only text, but graphics too on it.
The main issue is the price - a standard size, 1602 LCD compatible module with this controller costs about $6.
But, there are some other LCD modules with same hardware specs, but with different controller, which are far cheaper - like module using SBN1661 controller can be bought for 75 cents.
Back to SBN1661, while it has 8 bit and RS/E enable pins as HD44780, it seems not to be compatible with LCDOUT, since it has separate pin for DATA/ADDRESS selection.

So are there any other, non HD44780 LCD controllers, besides the ST7920, which can be used with LCDOUT statement? I only know WS0010, but it is OLED, not LCD....