At some point, though, the throttle response time for the descent engine was improved from 0.3 seconds to 0.075 seconds, but the ICD was not updated. So at least Apollo 10-13* all flew with 0.2 seconds of compensation. As it turns outs, the throttle was just barely stable with this much, and if Don had implemented the specified 0.3 second compensation it wouldn't have worked.
Apollo 15-17 (and likely Apollo 14) all had this issue corrected. You can see the difference in the constant THROTLAG comparing the Apollo 13 [2] and Apollo 15-17 [3] lunar module source.
* We haven't yet found a copy of the Apollo 9 or Apollo 14 flight software, so I can't definitively say that either had the error. We do have Apollo 5 source, but THROTLAG, the constant in question, does not have the same name there, and I'm not sure what the equivalent value is.
[1] http://www.doneyles.com/LM/Tales.html (towards the bottom)
[2] https://github.com/virtualagc/virtualagc/blob/master/Luminar...
[3] https://github.com/virtualagc/virtualagc/blob/master/Luminar...