As I cant see how the queen would be under the lug to start with, I therefore assume the worry is that she might go under it after you have lifted it.
The queen can be anywhere at any time. Especially with A.m.m. types, which are much more likely to be runners, it is not at all uncommon for the queen to be moving between combs or just making a rapid exit from the working area, by using the gap between the end bars and the side wall as transit route. If she is in that area and you shove a tool of ANY kind in there without seeing exactly what is going on you risk nipping bees, one of which might just be the queen.
Bear in mind that, relatively speaking, we are doing vast numbers and see things many of you may never see in a lifetime, or at least over a large number of hive seasons.
Introducing a J (or any for that matter) tool into that area HAS resulted in dead queens. Not many, but it does not need to be many to make the economics skewed against the practice.
No bees get under the lugs? try working bees, esp black ones, with bare hands for a few weeks, and see how many nips you get on your fingers when you encounter a bee that has wandered into that area.
What type of hive tool you, as an individual, might use is entirely up to yourself, it is not a big deal. As with so many other aspects of bees the effect of a certain item or its use vis a vis an alternative only become apparent over a large sample size. Over small numbers you do not notice or it is insignificant.
There are so many examples of that, where what is on offer or is conventional is actually not the best, and only over a big sample size does the truth emerge.
Things most will never notice include such things as hive tool type and minor queen loss factors. If it happened to say 20 hives only.............less than 1%.......the cost is into 4 figures.
The biggest single benefit was doing away with the National hive unit we had.............working bottom bee space boxes costs time and money, a team could do between 20 and 40 less hives in a day at the same cost, and the attrition rate of long lugged frames ran at about three times that of short lugged. All items of gear less simple and higher cost. Primarily in time and fuel, but it cost £7.40 extra to run a National as compared to a Smith for a season. Not a vast sum.........but multiply that by 500...........then the penny drops about apparently small things that add up to a lot over a big sample. On an amateur scale none of this matters as you are not into having to think of time/cost analyses. As soon as you go commercial these things all count.
The list of things of this nature is a long one.