Gym plan critique

This is a little bit unclear to me: Sorry.

Are you saying 300-500 calories of bike or cross trainer 4-5 days a week, plus 3 days of weights? You say "split": Does this mean she'd be hitting each muscle group once a week, 3 times a week, or something else?

It sounds like she's fairly new to the calorie restriction (whether counting or not, it's still restriction, right?). Do you have the slightest idea how far under her maintenance calories she's been eating, even in gross terms, i.e., low enough to cause aggressive loss, or relative more slightly below former habits so slow-ish loss? Would she be eating more if she exercises (I understand she's not counting)?

Is she is as new to exercise as to calorie restriction, or has she been active (how much?) and looking to do more, or someone who was active a few years back and is resuming? How old is she?

A few thoughts:

If she is new to exercise, either brand new or resuming after a multi-year gap, I think this routine would be too much, too soon if added all at once. I'd suggest phasing it in more slowly, with at least one recovery day in between workouts. As she starts finding that less challenging, more can be added. For similar reasons, I'd start with mild to moderate intensity and duration. Specifically, when the cardio is phased in, I'd start with time-limited segments, like half an hour max.

If she wants to lose 20-25 pounds, I'm guessing she's not substantially overweight. If she's an average-height woman, 300-500 calories of cardio is quite a lot, especially for a start. (I'm 5'5", mid-130s pounds, and count myself something usually in the upper 200s to low 300s for a 45-minute rather intense spin class or an hour of on-water rowing (of varying intensity, but sometimes quite vigorous). At a weight in the 150s to 180s, I might get upwards of 400 calories for the same sort of workout . . . but at that point I was already experienced at both modalities, so working quite intensely.

If new, I'd maybe start with two days strength, with perhaps a light cardio warm-up, and one day of just cardio (at a manageable steady state intensity), and put recovery days in between. I'd maybe even consider starting the first weight workout with 1 set of 8, going to 2 sets the next workout if that went well, etc., to ramp up to the 3 . . . but I admit my biases are to be quite gradual as I'm pretty old (63), and any injury/setback takes a long time to recover from. I'm not suggesting 400 years to phase in, but rather starting on the light side for a week, then assessing how she feels.

I'm not any kind of personal trainer (some education in rowing coaching is all), but was a relative exercise beginner myself in my mid-40s, and a phase-in process was quite helpful to me, from the standpoint of it feeling fun/rewarding/positive when working out, and not cumulatively too fatiguing. I'd add that I wasn't even trying to lose weight then alongside exercise, so was starting from a less potentially depleted point.

I don't know exactly what her circumstances are, nor what you're looking for, but those are just some off-the-cuff thoughts.

Best wishes to you both!