The repeat sleep study may or may not be necessary. The weight loss, although not large, may well have improved your previously borderline sleep apnea and, if that is so, you would most likely also experience less daytime sleepiness, feeling well-rested on awakening in the morning and find that your concentration has improved. If you have experienced any of these signs of improvement, you may not need another sleep study. If you have not experienced improvement, another option would be to lose 10 more pounds and then have the repeat sleep study.
The answer to your question is yes, there is a relationship between asthma and apnea to the extent that many individuals have significant improvement in their asthma control in response to control of the sleep apnea. The same type of cause and effect relationship exists between reflux and asthma. You might want to wait for improvement in your reflux to see if that is accompanied by improvement in the asthma.
Before agreeing to another sleep study, you might ask the pulmonologist his opinion of the improvement in your symptoms and whether such evidence of improvement might negate the need for another study. He/she is in the best position to make that judgment and, if he actually deems the second study to be of value, he should be able to explain the rationale behind his thinking.