You didn't make it clear whether she visits WITH her owners, how long
she will be with you for or whether the owners have this problem at
home, so, because she visits regularly, I'm pretty much going to outline how we housetrain new dogs and puppies in our house, even though she's not "yours". If her owners are having the same issue, you could maybe pass it on to them - if not, you would likely only need to go over this once or twice when she visits for her to realise that the same rules apply HERE, as at home.
First of all, no dog is "old enough to know where to pee". It's not about age, it's about whether they have been taught. As she is a rescue, it is quite possible that her first owners never house trained her properly, so it would be a bit like no one ever teaching you to read and then one day someone says "Well, you're OLD ENOUGH to know how to read!" 
Another thing to remember is, lots and LOTS of dogs regress in house training when they go to a new house, or even just visit a new house. Just because they can't pee AT HOME, doesn't automatically mean they can't pee inside ANY HOUSE. Dogs do not usually generalise very well, so this is actually very common.
A lot of dogs also regress in house training when something stressful happens - like moving house for example. This is because anxiety lessens the control they have over their bladder and bowels, and with some dogs, its a kind of marking and is linked to nervousness.... like, they reassure themselves by surrounding themselves with a very familiar scent; their own.
Finally, it's not clear from your post whethr she does actually GO every time
she is taken outside but is still having accidents, or whether she
doesn't seem to undertsand that she is meant to do it outside. If she is peeing very frequently and/or seems to have little bladder control, it may be a physical problem which is causing this, like a UTI. Do you know if her owners have had her checked by a vet for this?
Assuming that a medical problem has been ruled out, it sounds like Lady fits into quite a lot of these categories (a rescue, visiting, possibly stressed, possibly never trained properly in the 1st place) and add to this she is a small dog (therefore with a smaller bladder) it's really no surprise that she is struggling with this.
The very first thing you need to do is take away any opportunity for her to pee in the wrong place. So:
- Tether her TO YOU
- WATCH her very closely
- Take her out FREQUENTLY, especially after eating, drinking and sleeping, and long periods of chewing or playing. (You don't need to be outside very long, just a few minutes at most).
The second thing you need to do is make CERTAIN that your carpet is not harbouring any doggy-pee smells that are encouraging her to go back and use it again. Lots of regular cleaning products just don't do the job properly - OR they smell like ammonia to the dog anyway. You need an enzymatic one, designed for pet-messes.
The third thing you need to do is communicate to her the CORRECT place for her to pee, and just how PLEASED you are with her when she gets it right. How to do this depends on the personality of the dog and what they like best.
Take her outside as often as you can - every half an hour is good, but every 15-20 minutes would be even better, initially.
Keep her on a lead and walk about for a few minutes, to encourage her to "go".
Some dogs just CAN'T do it if they feel "watched" - in a lot of cases this is because they have been punished for peeing in the WRONG place before, and have simply decided it;s better not to do it in front of humans. So you may need to make a pretense of NOT watching her, even to the point of using a long line to give her more freedom and turning your back on her, using a hand held mirror to watch for when she "goes".
If no joy - that's fine, just take her back inside but watch her even more closely, keep her tethered to you (so she can't sneak off!) and resolve to try again in 5-10 minutes, or sooner if she shows any signs.
If she does go, then you might want to say a cue-word (like "hurry up" or "go pee" or whatever) AS she is going. If her owners do this, find out what word they use and use that. After a short while, this can be used to prompt her to go when she IS outside (and is very helfpul if it is raining for example).
The moment she has finished, step up close to her and pop a tasty treat in her mouth. Don't call her - WALK UP. You want her to KNOW what the treat is for, and it's not for coming to you 
(A note about treats: the treat should be the tastiest treat imaginable. Something soft and moist and stinky for preference. Keep this for "good potty" ONLY. This will make her work extra hard to get it - ie, once she twigs that she gets it for peeing outside, she will try to hold on and get outside if at all possible )
Now that she has peed and got her treat, don't forget to PRAISE her If she is not a nervy, shy dog, you can THROW A PARTY to let her know how THRILLED you are that she "got it". High pitched voice, lots of luv-inz, praise, petting, jumping up and down, yay! The neighbours will think your barking, but it will save your carpet. With some dogs, this doesn't help, because they are just too nervy and it makes them more neurotic about toileting. In which case, just give her lots of petting and praise her in a warm voice and SMILE at her. Your response to a "goodpotty" depends on her personality. If in doubt, just go for the quiet petting - she will still "get it", especially if the treat is a really yummy one.
If she ENJOYS play outside then play a fun game, and if its SAFE to do it, let her off the lead. A lot of dogs learn that peeing ends the fun so they try NOT to go when outside, because they don't want to come back in. If she just wants to get back inside then go back inside fairly quickly once she has been. In both cases, you could give her some limited freedom indoors immediately after peeing in the right place - so, no longer tethered, but keep her in the same room as you for now, so you can continue to watch her.
If she has an accident - interrupt it if you can and take her to the right place swiftly and calmly. REWARD her for anything she does out there, as above! Then put her out of sight while you clean up. Remember the enzymatic cleaner ) Soak up some of the pee in a paper towel and transfer it OUTSIDE if possible, and let her see and smell that. Never punish or scold her for incorrect toileting.
You might find it helpful to keep a pot of her treats near the door with her lead, so you don't forget to grab a couple on your way outside, and you will have them on you at the crucial moment. Treats delivered after the fact are unlikely to be effective.
Hope that helps.