I wouldn't do it. I'd push more towards practicing (and good instruction from paid instructors) with more capable rounds using top quality holsters and belts. I have no doubt a rimfire can and will be deadly. I have questions of how well it would stop an attack compared to larger calibers with more velocity.
If she handles the LCR weight and size well, why not grab one in .38 special? I would feel much more comfortable with 5 rounds of .38+p than a sixth of .22 Mag. Look at frontal area. The .22WMR has a frontal area of 0.039 square inches. A .38 has a frontal area of 0.100 square inches. That's a total frontal area of 0.234 square inches for 6 rounds of .22 Mag and 0.500 square inches for the 5 shots of .38 special. Assuming both penetrate equally, the odds of hitting something vital is higher with 5 rounds of .38. From a surface area point of view, a 6 shots .22Mag gets you just slightly more surface area damage than two shots of .38.
The other side is that if penetration is equal for both, shot placement is still what's critical and having an extra round may save you if an extra person is in the attack. If six attackers show up and don't plan to leave after the first shot, I don't know which handgun I'd rather have.
Now look at a compact 9mm, say a S&W M&P9c. It holds 12+1 rounds. That is a frontal area just less than the .38, at .099 square inches. That gives you 1.287 square inches of bullet face (2.5x the 5 shot 38 and 5.5x the 6 shot .22 Mag). It also gives you more capacity which she seems to find desired. I know this is the revolver forum, but if capacity and size are two major concerns for her, I would look at a semi-auto. It's also going to be a lighter trigger pull. I find the smaller revolvers much harder to shoot well than full sized ones or double stack compact 9mm's. The LCR is a bit of anomaly and would be why I'd grab it over a small stock J-frame if a snub nosed revolver is the only acceptable solution.
There really isn't a revolver out there that has great capacity,fires a widely accepted SD bullet, is light weight, has minimal recoil, and is as small as most compact auto-loaders. If the autos are without a doubt eliminated from the list, I'd rather carry a 5 shot .38 special than a 6 shot .22 Mag any day. Personally, I'd rather carry a 13 shot compact double stack 9mm than either but if I only had faith in a revolver, it would certainly be in .38 special well before .22 LR or Mag.