Actually, lifting doesn't raise your TDEE as much as cardio does, it's not key to eating more.

But, you keep the same reasonable % deficit between doing one or the other, you'll lose more fat on the lifting because of the increased metabolism during repair.
Whereas cardio actually has a chance of burning muscle mass, even with a reasonable deficit.

3-4 big exercises is better than a bunch of isolation ones.

More cardio isn't needed for improved cardiovascular health, in fact there is a point of diminishing returns. Especially when in a deficit it can just plain add stress.

It's all the stresses that make fat and weight loss difficult.

My concern with routine is what do you want your focus to be right now, because unless that cardio is done certain way, I see it just impacting and preventing getting the most out of the lifting.

And all the cardio in the world won't improve a bad diet that causes atherosclerosis, though it may slow down the effects. But that much would also add a bunch of negative effects.

So know what their heart problems are a result of.

And the recommendations to help cardio health aren't that much.
http://www.exrx.net/Aerobic/AerobicComponents.html

That's not bad at all then, just the level it's done at.

If anything, it's more the running on non-lifting days that would interfere with a good complete repair from the lifting.

If you can run in the Active Recovery HR zone, which usually means no additional load being put on the muscles, just blood flow, you can still jog on day after lifting days. That HR zone is badly called the fat-burning zone too.

If you want to do some faster running on lifting days, make it after a good lifting session, and then go whatever pace you want. Repair is going to happen next day anyway, so you may be slowed down a bit.
But don't do it before the lifting. Tired muscles lifting to almost failure is different response than fresh muscles. Can't lift as heavy and put as heavy a load on them.