Sorry I'm so late to this thread, Not sure how I missed it!
The only thing wrong with your plan is that most ERs have never heard of these fish or their venom so at the very least you should bring the latin name of the animal so they can quickly research it and start necessary treatment or better yet have a deep understanding of the venom, how it works and how to treat it + having all of that written down so you can take it with you in case the reaction effects your ability to explain to the doctor what happening and what they need to do. Just a heads up though most venoms that aren't toxic enough to have an antivenom are usually just treated symptomatically. If your keeping an animal that needs an antivenom like a stonefish you need to have it on hand and similarly be able to communicate what it is and how to implement unless you live in a part of the world where practitioners should already know this like Australia for example (although its probably still not a bad idea).
No fatalities have ever been reported from a lionfish sting as far as I know, Its actually pretty mild venom in comparison to some other scorps (stonefish are the most potent by far, stingfish and waspfish also have venom of some significance). I was stung by a dead lion after I speared it when I was in the Bahamas (where they are invasive). It was a very mild sting, the spine barely went 1/4 of inch into my finger and it burned but compared to other stings I've received it really wasn't that bad. I got stung by a two inch Synodontis eupterus once (a species of African freshwater catfish) and that hurt much worse, it was like a red hot pin was lodged in my finger for 2 hours before it started to improve, mind you I was unaware of the hot water trick at the time I was stung.
Ocean catfish of all kinds have a nasty venom, my brother was stung by one in Florida when he was 10 or 12 and the pain alone sent him into shock. Coral catfish that you see at your pet store have been recorded to cause fatalities. However just because a venom is "mild" does not mean it's not dangerous, everyone reacts to venom differently. Thats why I'm still typing this despite being stung by bees on several occasions throughout my life while others are not so fortunate to survive the same encounter. Also just because you haven't reacted to a venom before doesn't mean your immune or that you won't react differently the next time. Although I'm unaware of this occurring in marine animals, some venoms desensitize your bodies response meaning that very sting you get from a certain animal makes you more and more likely to have an allergic reaction.
I'm sure the outline below will seem very excessive to many you and that because it is, these our guidelines (to the best of my knowledge) developed by a community where death is a very likely outcome with or without treatment if you are bitten or stung (venomous snakes, scorpion etc). The worse case scenarios are the ones you need to consider and plan for the most. Again I'm sure this seems excessive for the relatively mild venom of our aquarium residents but I'm sure to all the people who are looking down on this because of the venom of an animal they kept- this isn't nearly comprehensive enough.
Any venom demands respect and part of that respect means having a plan. That plan should include at least some of the following:
Understanding the venom of the animal you're working with, what kind of toxin it is, what parts of your body it effects, potency information, symptoms of envenomation etc. Also making sure that all residents in the household understand the animal is venomous, the potency and what to do if either you or they are stung.
Proper labeling, typically the animals latin name and several stickers of the "CAUTION [HIGHLY/MODERATELY/MILDLY] VENOMOUS" variety depending on the species accepted or understood potency. Skulls and crossbones are a nice touch since they are nearly universally recognized. Notes detailing the delivery system are also a good idea "CAUTION VENOMOUS SPINES" or "CAUTION ABLE TO SPIT VENOM ALWAYS HAVE EYE PROTECTION" etc. Having labels in both your countries first and second language is also not a bad idea.
Properly secured enclosure, out of reach of wandering hands or better yet kept under lock and key (this one is harder to do with an aquarium though so I personally wouldn't bother unless I had children in the house or was keeping something highly venomous).
Having an Epipen (or antivenom where applicable) in close proximity to the aquarium, having its location well known and clearly labeled in case you're unable to inject yourself and making sure to discard and replace them once they have expired.
If you are stung and your waiting to see how your body will respond to the venom text or call someone who lives close by and tell them that you have been stung and ask them to come over to stay with you until your sure you aren't going to have a serious reaction to the venom. This is incase the venom renders you unable to call for help or take the steps needed to treat yourself with an epipen. Worse case scenario you have someone who can rush you to the hospital. DO NOT try and drive yourself to the hospital unless you live in the middle of no where. If you'r dying from the venom of YOUR animal that is YOUR fault and a consequence you've accepted by deciding to keep that animal. You have no right to risk the lives of others while trying to save your own by getting behind the wheel with a venom in your system.
I'm not trying to discourage anyone from keeping these amazing animals and sincerely hope I haven't. I'm saying this because its our responsibility as the keepers and stewards of these animals to understand, manage and prevent the risk that they can present to ourselves, our family and our hobby as a whole. Also the above is geared towards dealing with being stung after the fact, prevention is always the best way for everyone to stay safe. Using magnetic scrubbers, longer syphon tubes for water changes and gravel vacs, having a temporary barrier while your working in the tank, making sure all venomous fish are accounted for, constantly checking their position and most importantly not allowing yourself to get complacent or skip steps in your protocol out of convenience or laziness. It is entirely possible to keep these animals and never have an incident but you must have the self discipline to do so.