What kind of brain damage are you implying? Maybe from damage from benzodiazepine dependence? I am not aware of data that points to "brain damage" from normal doses of LSD. If somebody is prone to psychosis it can trigger it or make it much worse, but otherwise I don't think LSD causes brain damage. Person can be psychologically damaged from taking LSD if setting is not carefully chosen or if one gets stuck on issues that he can not process, but if setting is well controlled, LSD is really LSD and not some RC than person it is left with a substance that is potentially beneficial even if the mindset is not perfect. Mindset is always important , but rarely anybody has it perfect and all one can do is to respect the experience and try to let it go if gets stuck. Maybe I am wrong, but I am not aware that regular dose of real LSD can make an actual brain (tissue) damage. I am not saying anybody should take it as it is really potent substance which should be taken with great care and a good dose of humbleness. I do not want to say fear, but great respect is prerequisite for taking strong psychedelic.
From what can I read in between the lines, it is not first time OP will take LSD, but problems may arise from agoraphobia that will be magnified. I would not advice somebody with agoraphobia to take LSD and then go out for a walk. It could lead to severe psychological distress that could become even greater if the experience goes wrong. There is always potential for resolving psychological issues when psychedelics are taken, as they confront us with ourselves, and if we have nowhere to hide we will either make improvement or create even greater issue. But that is double edged sword of psychedelics - they put you in the position where you can resolve some block that otherwise would take ages, but as those issues are by definition hard there is no guarantee that result will be positive. If it was me and I had some big issue I would not try to break through it with LSD. Psilocybin is much better candidate for resolving issue like agoraphobia. I must repeat that this is not an advice but an experience I share.
Now finally, regarding combining clonazepam with LSD I am not thrilled about that idea. Purpose of LSD should be to have intense experience that you can remember, and if you are diluting it with benzodiazepines than that should give you an answer what to do. But then again, some people take low dose of benzodiazepines to take the edge off. Anything more than 0.5mg clonazepam and I would say that it is not worth the potential complications. on the other hand clonazepam could be very handy if you wish to, maybe not abort, but slow down the experience if it goes the wrong way. But as clonazepam is not antipsychotic it will not stop the trip completely so you should take that into consideration.
I am being very cautious, but if I had to answer i would say that clonazepam will dull the experience but it will not kill it. It may make experience not worthwhile if you go above 1mg clonazepam, but if you need that much to control the LSD trip than I would not take LSD. Or take low dose and have clonazepam in the pocket "just in case", because the fact that you have 4mg of clonazepam in your pocket could give you the peace of mind by itself.
It can go in every direction and I do not want to give opinion should you take it or not. LSD is to powerful of an agent and that makes thing tricky. But I sure wish you all the best!