How can I get very high speed from a FTDI chip?
I have tried with FT232RL with UART in 230.4kbps but I want much more than this. Will I need some other different speed?
The pc sends 1 byte on mcu, mcu writes this byte to an lcd 1602 and sends two bytes as response back to pc witch corresponding to an adc conversion.
Your problem isn't bandwidth then, but rather with latency. People think of the USB bus as being very fast, because for most purposes, once it gets started moving packets of data it can move a lot in them quickly.
However USB is also extremely slow in one respect: it takes a comparatively long time to start moving a packet of data. When the data comes in small chunks, and sending new ones depends on receiving the response to previous ones, you constantly suffer that latency, and your data rate falls far below what the USB or continuous baud rate can support.
Typically the opportunity to start a transfer comes about 1000 times a second, and if you only send one byte per transfer that means your effect data rate is a mere 1000 bytes per second (the 1980's called and they want their dialup modem back). But actually, your progress is even slower, as you need to send two bytes in the other direction before you can do it again. So likely you are accomplishing fewer than 500 cycles per second...
You need to redesign your protocol so that you can move large amounts of data in each direction without requiring confirmation - it's waiting for that round-trip over the USB bus that is killing your throughput, not the actual baud rate. By itself, a chip with father baud rate or USB version won't actually help.
Your existing hardware may actually be fine.