Hi and welcome,
There are actually different types of brain lesions with the most common being caused by Cerebral small vessel disease, which is basically an umbrella term with alternative names seen on MRI reports being Small vessel ischemic disease, White matter disease, Periventricular white matter changes, Perivascular chronic ischemic white matter disease of aging, Chronic microvascular changes, Chronic microvascular ischemic changes, White matter hyperintensities, Age-related white matter changes and Leukoaraiosis.
I can't tell you if any of the other types of brain lesions disappear with 100% certainty but i know that MS lesions definitely can, MS lesions come and go because of remyelination or they have shrunk to a size the MRI couldn't detect...
Which brings up relevant facts with MRI's which can also skewer results, and it's more of a technical issue than with the lesions themselves.....a 3T MRI will pick up somewhere around 20% more than a 1.5T MRI can, the software can even make a difference and even stronger MRI's that are typically used in research, which off the top of my head i think are 7T's will pick up even more because it's about 5x stronger than what hospitals and clinics usual have....basically the stronger the MRI and the better the software the MRI has can make a significant difference in how much the MRI can pick up.
One of our well loved retired CL's Quix experienced the above situation herself before she was dx with MS, to cut a long story very short, the lower strength MRI showed zero spinal cord lesions but when the spinal cord scans were run on a stronger MRI it actually showed she had 6 spinal cord lesions.
Another MRI issue can be as simple as the size of the slices were wider, so the lesions are still there but the bigger slices missed the lesions, to give you an idea the recommended slices to detect MS brain and spinal cord lesions is less or equal to 3 mm, optical is less or equal to 2 mm but the standard MRI slice is 5 mm.
And yet another MRI technical issue are false positive lesions that fall under the term UBO's which stands for Unidentified Bright Objects and the only way i can explain what this is is to think of what use to happen sometimes when you took a photo with a flash and certain parts in the photo have spots or flashes of white, which are not there in reality but are a technical glitch.
I really hope i haven't confused you and did somewhat provided you with a little insight in to how lesions can for various reasons be there on one MRI and disappear the next!
Try if you can to be open minded about what's going on, hopefully after you've seen a neurologist you will get a better idea, let us know what happens...........JJ