She had reconstructive knee surgery last year and I really want to get her to squat so she can strengthen up her legs again.
StrongLifts 5x5 works for women just as it works for men. Her progress may be a bit slower because women's testosterone levels are much lower, but she will gain strength and muscle. She will also lose fat although, again, slower since women are smaller than men. There are female StrongLifts Members who have done SL5x5 with training logs, example Frotabaga, Leida, 5inthehall, etc.
I've trained females, although much less than guys obviously because more than 93% of StrongLifts' audience is male. That's why I can't provide you with success stories - I've never bothered to collect them (you can misinterpret and call me misogynist or whatever, but the facts are that while about 51% of the population is female, there's 93% chance you're not. So I act accordingly).
The best advice I can give you is to watch out with phrases like "I want to get her to...". I think you mean it well, and it's most likely what she needs with her knee issues - (since she's female, my guess is it's ACL related). Yet I'm sure you know the saying - you can lead a horse to water, but you can't make it drink (I'm not implying your girlfriend is a horse...)
I was asked if my girlfriend lift weights. No she doesn't. I never tried to get her into lifting weights, and I'm not going to anytime soon. Frankly, I think she should be doing some sports, but she's just 22 (yes I'm 30, sue me), weighs only 110lb at 5'6" (she's Asian, sue her) and eats healthy (high protein/veggies, nothing like that Chinese take away crap). So what would her motivation be?
Getting someone started is easy. Getting that same person stick with it is a different game. It is common for guys new to lifting to get enthusiastic and try to get everyone else also into this. But the guys who've been doing this for a while, and who have trained with dozens of people with only a handful sticking long-term, they eventually realize that you're pretty much on your own. StrongLifts Members know that few people, not even their gf/wife, "get it". And this is one reason why they come together inside the StrongLifts Community.
Personal examples - my mom had her meniscus removed a couple of years ago. Months of PT later, she still had knee issues because the PT was an idiot. I got fedup with hearing her complaining about her knee and - breaking my rules - convinced her to do Squats. She never sticked with it. My brother trained with me last year, was pulling 300lb within months, then he quit ("no time"). Now he wants to resume because he's getting fat. Well, I'm already training with someone else. My dad should be doing Squats because he's starting to lose mobility now in his late 50s, but he doesn't want to listen. They all say I'm "more disciplined", even though they know I was too lazy to do sports before I got into lifting (dad and brother played soccer for years, I never did anything).
So don't get pissed if she doesn't share your enthusiasm or stick with it. I don't feel responsible for someone else not doing what I think they ought to be doing to get or stay healthy, nor will I let someone sabotage my training, and neither should you. You can misinterpret this too, that I'm selfish or don't love my parents/brothers/gf. But I just know how people are, and I tell you - it is NOT your fault if they're not as motivated as you are. The secret is finding someone who is motivated to start with, not trying to motivate them into it.
The fact that she's curious about StrongLifts 5x5 is a great start, but it's not a guarantee. I'd treat her like all the guys I've trained with it: invite her to train with me, exactly like I say, with no bullshitting during the training. If she shows up again the next time, she passed the test and you may have just gained a quality trainingpartner. If not, let her train alone to "tone up". Be warned, 80% of people won't show up again. Remember that is NOT your fault at all.