Can I still do 5X5 Stronglifts while trying to lose weight?

I've lost weight while doing stronglifts.

I agree that you seem to be doing an awful lot of cardio though. If you enjoy it and are eating enough to cover it, go for it... but it's not really necessary to do that much.

YES YES YES! It might slow your weight loss down by a bit but lifting weights will make you LOOK so much better as you loose. Just make sure you dont stress too much on the scale, take measurements! This time last year I was a skinny fat 137 (im 5'8 large frame) I looked very thin but I was soft. Now Im 143 lower bf% and I have around the same measurements but look much much better.

The only possible issue may be your cardio. Two hours twice a week on top of weight training seems a bit excessive to me. You may want to consider cutting it down to under 30 minutes of HIIT when you do cardio.

That's my problem I guess, in my head I feel like the weight training doesn't do anywhere near what the cardio does, so I can't get my head around not doing a lot of cardio. I use a HRM, and with my weight training and little amounts of cardio I only burn about 300-400, on my big cardio days I can burn up to 1500cal, which is where my issue in giving it up is I guess.

I'm guessing with that much cardio I may need to raise my daily calories though, at the moment I try and average it every day at about 2100, and don't eat back exercise calories. Averaged out over the week it works out to be about 1500cal a day when exercise is factored in..which is the amount it gives me when I set my goal at 2lb a week loss.

How much do you have to lose?

If you are losing weight at a steady rate now, then keep doing what you are doing. But if, in the long term, your weight lose stops/stalls then you might want to consider eating more. IMO.

The less you have to lose, the smaller your deficit should be.

Absolutely! You can gain quite a lot of strength without ever putting on additional muscle mass, and lifting while you're losing weight will help you to lose just the fat, for the most part, without taking a lot of your existing lean mass with it.

You will eventually plateau in your strength gains in this situation, but that's fine. Switch to a more advanced workout structure (something that cycles between light and heavy weights over the course of a week or two) to maintain the strength you achieved while possibly making some more modest, gradual gains. If you so choose, you can eventually start eating at a calorie surplus to allow your body to build more muscle and progress from there.

Regarding calories burned with weights versus cardio, it really doesn't matter. If you're maintaining a reasonable calorie deficit, then you're eating more food to support all that exercise, anyway. You can cut back on the cardio and just eat less food to make up for it, keeping your daily deficit at around 500-1000 calories (or 250-500, if you're getting close to your goal and need to nudge through those last few pounds).