Did he force them to assimilate with his people or did he allow open practice of the conqueree's culture?
Those conquered by Liu Bang prior to the defeat of Xiang Yu were from similar cultural backgrounds. The fact that Xiang Yu could reasonably think that he was surrounded by soldiers from Chu singing Chu songs indicates that Liu Bang did not practice forced assimilation, or at least had no reputation for doing so.
After the unification of the empire, Liu Bang was generally too busy killing off his old generals to do much conquering of different cultures. The only contact with foreign subjects that I'm aware of was with the southern and eastern Yue, both under peaceful circumstances. In both cases, local leaders were allowed to continue on as Kings (in the case of eastern Yue, this entailed a change in title from Chieftain) with a great deal of autonomy.
Source: Records of the Grand Historian by Sima Qian, translated by Burton Watson