There isn’t. See Python’s standard library – is there a module for balanced binary tree? for a general discussion of the equivalents of C++ tree containers (map, set, multimap, multiset) in Python.
The closest I can think of is to use a dictionary mapping integers to counts (also integers). However this doesn’t get you the keys in order, so you can’t search using lower_bound. An alternative is a to use an ordered list, as suggested by others already, maybe a list of (integer, count) tuples? If you only need to search after you’ve done all your insertions, you could use the dictionary as a temporary structure for construction, build the list after you’ve done all the insertions, then use the list for searching.