Using an arduino pin to give pwm to a solid state relay which has the heater connected to its o/p(350W is heater wattage).
PWM for AC heater..........
Or did you just mean its a ON/OFF switch with the pin output HIGH/LOW?
Heaters are electrically equivalent to small inductive coils with high current.
This is just a guess cause I don't know the wiring but if you are using PWM and this interference on the LCD only happens when the heater is on, then your wiring is causing it.
PWM is 3-60KHz, and if that is switching a 60Hz line, while controlling a high current, high voltage coil, there is going to be a lot of feedback spiking and dipping onto the AC line. Its hard to believe that any amount of switching on a heater with so little inductance could cause EMI directly (via air). More likely in my opinion is it these spikes and dips have no circuit to make until you turn on a light or fan, most other devices would have filters and small loads.
I have no idea what heater you are using, or if what I just said is whats going on. Using a cap will probably fix it, but thats kind of a band aid solution. If there is really enough EMI on a AC line or the air to mess with a LCD screen being powered from a DC supply, you have other things to worry about. All that interference will strain other devices and if there are high current spiking happening its not good for the wiring.