The K240 is a 600 amp contactor assembly. Since the the welder is hot all the time.
The contactor will make the weld circuit cold. Operates off of the 115 volt plug.
The LN 7 needs 115 volts to operate and can turn the contactor on and off so the welding wire is hot only when feeding. For what you want to do you have two choices.
1, just power the LN7 from the welder and use the wire hot all the time.
or 2, find a large relay (contactor) that can make and break 300 to 600 amps. DC
you can use a smaller one but you must size it to what you are welding.
You might look into the replacement contactor sold by profax / lenco for use in the LN25 wire feeder. its is a DC contactor around 300 amps. The coil needs 12vdc. so you can use battery voltage. But as you are building it . power the contactor on 12vdc and measure the temperature of the coil. If it gets hot you will need to lower the voltage to the coil. One way is to switch in a resistor and drop the voltage to 8 volts or less a 1/2 second after applying the full 12 vdc to pull in the contactor.
This is called pull in and hold voltage. Can be done with an electronic timer or the old school way we modified a control relay so one arm made contact just before the other. adding or removing the resistor. over all you are trying to make the LN7 work like a LN25.