The fact that you feel burning at a certain point in intercourse and not from the start can mean a couple of different things. It is possible that you are allergic to either latex (if he's using a condom) or to the lubricant.
The fact that the reaction doesn't happen immediately but occurs after some time may be related to the fact that it takes your body some time to react to the offending allergenic agent. Another possibility is that your urethra is irritated and ongoing thrusting may aggravate the irritation.
Check to make sure that you don't have a silent bladder infection. Also make sure that you don't have a yeast overgrowth. One common symptom of this is urethral symptoms. Also make sure that you don't have a vaginal infection, which can cause the sensation of irritation and burning that you describe.
If everything checks out, the last possibility is that the burning feeling is associated with sexual arousal. Some women describe feeling burning sensations and various points during sexual intercourse.
These sensations may be the way your body manifests sexual arousal. If the sensation passes and doesn't interfere with your pleasure, then it shouldn't be cause for concern.