Hi there!
I quit smoking in May 2011. Let me start off by saying I had only been smoking for 3 years so my advice may be a little off but I will share my experience and maybe it will help you! When I decided to quit smoking, I also decided I wanted to get into shape. I needed to change my entire lifestyle because up until then I was eating fast food several times a week, smoking about a pack every 2-3 days and not taking very good care of my body. Like you I also had aspired to get into running.
For the first month I found my cardio was crap. I could barely do anything without being out of breath, on top of being over weight my lungs just couldn't keep up. I would jog for only about 30-40 seconds and have to stop to get air, it was a great wake up call. Instead of jogging right away I decided I needed to do something less strenuous, so I did some work out DVDs and video games on my xbox kinect. It worked wonders, I lost weight and was slowly regaining my lung function. It took 1.5 - 2 months of this before I found myself able to move onto something a little more intense, when I did I stepped it up to a step aerobic tape I had in my house. I started with the smallest step possible and over the course of a month I was onto the biggest step and easily doing the advanced moves.
I began running on the treadmill 6 days a week and let me tell you, it was hard! Although I could run for a minute or two straight after that I was gasping for breath and had to take a long recovery walk to let my lungs catch up. Even though it was hard, I found it getting better even week by week. When I started I was jogging at a speed of about 4.3 (super slow) with no incline and it took me 80mins to run 3 miles. Its been about 2.5 months of using the treadmill now and I can run about 10-20mins straight, at a speed of 5.5-6.0 with a 2% incline, it takes me 55mins to run 4 miles. It is a significant improvement from before. My goal is to one day be able to run the entire time but for someone to essentially killed my lungs I do okay and am in no rush
Your lungs will definitely allow it but you have to remember to take it slow, as slow as YOU need to. Your lungs have been through a beating and will need time to adjust and clean themselves off. I think the best advice I have for you is to take it slow but keep your goals in mind, even if you are only improving by seconds you are still improving
Good luck! I hope I helped.