Arduino Nano and a 3.3v Ethernet shield
Just get one with a 3.3v regulator on it. PS logic levels are allowed to be 5v.

DHT22 and LCD will also work fine on 3.3v so, alternatively, you could also get a 3.3v Nano.

The resistor value for the DHT22 depends on the length of wire between the DHT and Nano. Just buy them to be sure, or get a breakout board that already has them on the board (along with a capacitor, which is nice).