Cab-Lab 4 might not connect so you can monitor the IRs being created, but it should output IRs that are compatible.
Maybe
@Admin M@ has some ideas for a workflow?
Workflow:
Run two channel strips set to monitor input in your DAW, with one having the Cab Lab 4 plugin instantiated and other without Cab Lab 4. Monitor through the one with the plugin instantiated to dial in your IR, and then monitor through the other one without the plugin to listen to it after it's imported into the Axe II and added to the Axe II's preset's Cab Block. Be sure to mute the channel strip you're not using!
1) Run the Cab Lab 4 plugin in a DAW and monitor your Axe II through the DAW and the Cab Lab 4 plugin with the Axe II's preset's Cab Block bypassed.
2) Dial in your Cab Lab 4 creation via the plugin while playing your Axe II (while montoring only the channel with the plugin instantiated).
3) Save your new IR from the Cab Lab 4 plugin to your computer, and then import it into the Axe II, and finally add it to your Axe II's preset's Cab Block.
4) Finally, enable the Axe II's Cab Block and give it a play (while monitoring only through the channel strip without the Cab Lab 4 plugin instantiated).
I do it this way with the FM3 and Pro Tools, though this method will work with any DAW that can run the Cab Lab 4 plugin, and it works great as Cab Lab 4 doesn't seem to work well with the FM3 when it's using it's FX Loop, and of course it doesn't work at all with the Axe II or Gen 1 AFX's.
It sounds somewhat complicated at first, but once you're set up it's quick and easy to operate, so be sure to save your Cab Lab 4 DAW session for later use!
Pro Tip: Do it to a full track of your music at a monitoring level of around 85db or so.