Remember, we say here as part of DBing principles:
ACTIONS not words...
There are a few things to consider about this...
There is nothing wrong with clarifying with him that you need time to sort things out for yourself.
But in the same token, this is about you, not about him... you do not need to "protect" him by telling him WHY you become so distant from him...
Untangle yourself from that mode, because I think you protect him a lot, in many ways, and it may show up more than it is healthy for either of you.
Or... you will actually be using words as a way to manipulate him, that by saying you are distancing yourself, you are giving him advanced warning so that he will react and do something about it to pursue you... perhaps something that you might want... not a bad thing... just something to consider... ie. not his actions, but your intentions... in a passively manipulative way...
So if / as you transition into LRT, AS A WAY TO PROTECT YOURSELF and get out of the drama so that you are not reactive in your emotions (which showed up when you found out about the house)... the house is just a financially logistical thing, if you really look at it from a non-organic standpoint. It is when you put meaning to it... regardless of what ever meaning it may have for your H or his family or anyone else... this is about YOU putting meaning to it, which you may find you stop doing as you go through the LRT to detach...
Please continue to ask questions for clarity and to help guide you through this. We are always here to support you.