The running lag on each side is maintained in an internal register in that side, which are independently counted down each issue clock and are reset up as added lag is decoded. The difference in the contents of the lag resisters tells which side restarts first, or rather that is the effect, because each is independent and restarts when its private lag runs out. Of course, if the registers have the same value they restart together. In your example, because both are non-zero they both stall and the left counts to zero and the right to one. The next cycle the left (at zero) issues and the right counts to zero. The cycle after that they both issue.
This of course leaves the question of how to know the running lags at some random point of the code. The call operation saves the lags and return restores them, which takes care of calls. However, the debugger is more of a problem. The compiler statically knows when each half-instruction issues relative to the half-instruction on the other side and can put the relative lag in the debug info. However, if both are lagging, there’s no way (at present) to tell the debugger/sim to startup (or examine) one, two, … cycles before lag-out and issue resumption, and instead you see the program as of the first actual issue after the point you select if that point is in the middle of bilateral lagging. We could add a command to the UI to let the user set the lag point, but it oesn’t seem to be actually useful and we haven’t.