If you can only work out a couple days per week, you probably do both your lifting and cardio exercises on the same days. While that’s not ideal, you can maximise the benefits if you lift before you run. Here’s why.
As youtuber PictureFit explains in this video, it largely comes down to your glycogen, a stored form of glucose you can metabolize quickly for energy. Both lifting and cardio exercises require glycogen, and if you have too little of it stored in your muscles your workouts will suffer. Your lifting routine, however, will suffer the most because it requires quick bursts of energy provided by your glycogen stores. Cardio’s glycogen burn, on the other hand, is slow and steady, meaning you can train your body to do it with low glycogen levels, and it may even increase your performance over time.
Another factor at play is the body's production of certain enzymes during exercise. The enzyme mTOR is essential for muscle growth, and your body produces it when you lift. But AMPK, an enzyme produced by low-intensity exercise like cardio, inhibits mTOR signalling. So, if you do cardio first, the AMPK your body produces can decrease the amount of mTOR you produce when you lift later. That means less gains for you.
Lastly, you have to consider fatigue. Cardio often leaves your muscles with residual fatigue, which compromises your muscle force production. Your heart will be taxed too, affecting energy transportation in the blood stream. And you might be mentally fatigued from your cardio session as well. Basically, lifting demands more from your body in a shorter span of time, so it's best to do when you're fresh and energised.
That said, do whatever will help you stick to your exercise regimen. If running before lifting fits your preferences more, that's fine. But if you can help it, doing weights first is going to be more beneficial for you in the long run. Better yet, do them on different days so you don't have to worry about it. Or, at the very least, do them during different times of the day so your muscles can recover.