In Java8 functional style, how can i map the values to already existing key value pair

You can use computeIfAbsent.

If the mapping is not present, just create one by associating the key with a new empty list, and then add the value into it.

dataMap.computeIfAbsent(key, k -> new ArrayList<>()).add(someNewObject);

As the documentation states, it returns the current (existing or computed) value associated with the specified key so you can chain the call with ArrayList#add. Of course this assume that the values in the original map are not fixed-size lists (I don't know how you filled it)...

By the way, if you have access to the original data source, I would grab the stream from it and use Collectors.groupingBy directly.