Works after a couple of tricks and tweaks.
One major issue: the LCD driver seems not to be ILI9341. After trying many libraries for Arduino I checked the web address on the back of LCD PCB, the mcufriend. From there I found a couple of links to library files for 2.4 inch LCD. The library which worked for my LCD is MCUFRIEND_kbv, but that is not all... the library has a sketch named "diagnose_TFT_support", which reported via terminal that the LCD chip ID is 0x9595, which means that the line "#define SUPPORT_8347D" must be uncommented in MCUFRIEND_kbv.cpp file in library folder (see mcufriend_how_to.txt file for explanation). Thats it, my LCD works, even the touch panel.
Anyways, took about a couple of hours to figure this out, hope someone will find this helpful.
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