For lwIP, the board you mention does not have any problem; there is an RJ45 connector on the board.
For Modbus-RTU, the problem is that there is no RS485 interface on this board; moreover teh only serial interface signals that can eb accessed on the extension connectors (Arduino-v3 compatible) are Rx/Tx from USART6, but without any modem control signals. So the only possibility is to get an RS485 Arduino shield (like this one that will provide such an interface.
Then you will have to look at the various libraries that may allow to implement Modbus-RTU on an STM32 (or on an Arduino, but there will obviously be more adaptations to do); Anyway you will have to tailor them as you will have to use GPIOs to emulate the modem control signals of the USART (needed to drive the RS485 line drivers) that are not available on the Arduino interface.
Hope this helps,