I have not been able to figure out how to create the following filters in LR - any help will be much appreciated.

1) Display only photos that don't have a caption or don't have any keyword(s) assigned.

2) Display only photos that don't have a specific keyword assigned.

Thanks in advance,

Peter

2 is rather simple : Custom filter -> Text / "keywords" "don't contain" (enter your un-searched keyword).

1 will need a smart collection to have the two condition, I think : match "any" of the condition : "caption" "is empty" / "keywords" "are empty" .
If you want no caption AND no keyword, replace any with all.