Will I lose strength?

Power to weight ratio is more important than sheer strength in cycling, especially when it comes to hills.

If you drop 50 or 60 pounds (which is your goal), you'll have a dramatic difference in the amount of work over the course of however many thousands of uphill pedal strokes you might do on an average ride.

Good cyclists have very strong legs, but the power lifters in the gym aren't likely to make it up a long climb on a bike very easily.

Here's my experience, see if it helps: I'm a lifelong lifter, and started doing tris with a lot of muscle overlaid by a lot of fat.    I was around 230 lbs, and now I'm at 180.  I've continued to lift while doing tri training, and the strength loss has been minimal, if any.  I am squatting a slight bit less than I was at my heaviest, but otherwise I'm as strong as ever, and I seem to have retained the muscle mass as well.

My cycling has improved ENORMOUSLY over these two years, and it's due to losing the weight, as well as improving muscular endurance.  I have a much better power to weight ratio, and my power output has increased significantly, even while, as I said, my squatting strength has declined slightly.