I cannot quite make out the numbers of the chip in your photo, or the pins each circuit trace go to from the connector (you can check with your ohm-meter), but a quick perusal of the IC data aheet will soon clear up the issue. They may be I2C or something similar, or just GPIOs with a bit bang UART, or TTL level or CMOS RS232. It doesn’t look to be RS485 as no surrounding driver chip usually found if there is. You may even find a sample code section in the associated Application Notes that is often followed studiously by the developer that may offer hints for reverse engineering and interfacing. Usually chips of this size are PIC series from Microchip, and they may even be running Arduino code. The board may be an evaluation circuit that has been used as is. If being run from 5v, you may need voltage conversion for ESP chips. If it being used to drive the display, it may have control codes being received as well as data you wish to extract that may need parsing.
What is the LCD display part number it is connected to? This may also assist in identifying the protocol being used, or even to find application notes that may shortcut your research.
Update: have a peek at a similar exercise in reverse engineering at this thread that may inspire your approach.