There have been other extension cord discussions- search a bit and you'll find them. I assume that you mean the SP175 but other machines with similar outputs will have similar input requirements. In this case Lincoln says at max output on 230 volts the machine will draw 21 amps. You will probably seldom use max settings and since the duty cycle (30% at max) will give the extension cord a break too I would think number 12 wire will suffice. I believe the machine will compensate for voltage drop in the extension since it states 208v is also an acceptable feed but you should check with the salesman. Look at the plug on the machine, If it has 3 pins you need 3 wire if it has 4 pins you need 4 wire, either will be easy to find. A plug that fits the dryer outlet, a socket that fits the welder and careful wiring.
If you use the machine 10-15 hours you will probably only accumulate an hour or so of trigger time. 21 * 230 = 4830 watts for 1 hour is 4830 watt-hours say 5000 giving something to keep the fan turning while you aren't welding. 5 kilowatt hours around here cost about a buck.
Have fun-
Bill