I have allergies and asthma. Will targeted exercise help strengthen my lungs to make them a little more efficient?

Yes. Your asthma needs to be in good control. In general, swimming is the best overall exercise for asthma and will improve endurance, muscles, and strengthen your lungs. Tai chi will also help as will some martial arts.
Breath exercises. Specific breathing exercises have been shown to help asthmatics improve their lung function and decrease their use of rescue inhalers. You can watch on you tube specific breath exercises that help you expand your full lung capacity. Most of us breathe only using the bottom 1/3 of the lung, learning to use the full lung is important for all but especially people for lung disease.
Muscle efficiency. Your lungs don't become more or less efficient with exercise, but your muscles do. Exercise is good for everyone, especially those with heart and lung disease. If your disease is severe, you can start in a supervised setting.
Yes they help. Specific breathing exercises targeting lung capacity has been shown to be helpful to patients who suffer from chronic inflammatory lung diseases. These are quick exercises to increase total lung capacity, most of us only use the bottome 1/3 to 1/2 of our lungs to breathe. Patients with chronic lung inflammation use less. This can decrease rescue and steroid use over time if done regularly.