i want to filter the list

you want to filter the map so that only values (list) that contain the items are in the result ? or do you want to

map

over it filtering the lists ? for the former:

map.filterValues { it.any { searchQuery == it.propertyName}}

for the latter:

map.mapValues { (key, list) -> 
    list.filter { searchQuery == it.propertyName }
}

or similar

filter the list inside the map for values that match a criteria, and then if one of the lists that belong to a key was empty after this previous filtering for criteria, that key must also be removed

val filteredMap = map.mapValues { (key, list) -> 
    list.filter { searchQuery == it.propertyName }
}
.filterValues { it.isNotEmpty() }

maybe something like that ?