Complex sentence: It is traditionally believed that although he was supported by Capone, many members of the organization opposed his reforms as a faction under Capone rival Joe (Aiello) challenged Lombardo, calling for his withdrawal from office.
Split into simpler sentences: It is traditionally believed that he was supported by Capone, but many members of the organization opposed his reforms. A faction challenged Lombardo, under the leadership of Capone rival Joe (Aiello), calling for his withdrawal from office.