We'll need some numbers to be able to suggest anything useful. What's the output capacity of the generator (peak and sustained)? What current will you be welding with from the inverter?
Simple maths will tell you what the input current at the inverter will need to be (assume the inverter is around 80% efficient - most are better than this, but it's best to leave some margin).
For example, for MMA at 100A, you'd expect the output voltage to be about 25V (arc present, not OCV), so that's 2500VA. Which will need an input of 3125VA (allowing for that 80% efficiency).
However - when the arc strikes, the current will briefly be much higher than that, maybe even double for a fraction of a second. Even with an inverter rather than a simple transformer type welder. And that is why you need a generator that can either deal with sudden changes in load, or is big enough to provide it without the voltage dropping or the engine struggling.
Inverters and non-AVR generators do not mix well. The peak voltages developed by the generator when the arc is extinguished are capable of doing significant damage to the inverter's electronics.