Hi everyone!
I assume thats its possible without any problems in Marlin with standard RAMPS. Please say me exactly what I need to do to connect LCD with I2C interface..

Especially, I wont to know how I needed modify Marlin for I2C LCD...

Does anyone solved this problem?

Hi,

You might need to get one of these LCM 1602, some more details here
[henrysbench.capnfatz.com]
I'm using one to drive a 20 x 4 char over I2C, it's not on printer but IoT project but I think it's what you need to drive LCD display with Ramps board.

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Supporting 3D Printers with Parts and Build services.
Printer: Ormerod 2 (528.4) Duel extruder set-up with Aluminium X-Rib, RRPro Firmware v1.11-ch (2016-04-08)

This would be a great idea because it would free up a lot of resources and possibly allow for drivers/extruders