You might be able to learn if there were a relationship between your Daniel Rice and Lt. Benjamin Rice by going to the Bedford Co. Courthouse and Henry Co. Courthouse and look for Court, estate, tax and land records.
The Virginia State Library also has great resources in tax and Chancery court records.
Records concerning Benjamin's military activities won't tell you a thing about whether your Daniel is related to him, assuming that you have already checked Rev. War Pension Application Files to see if Benjamin applied.Occasionally if there were a surviving widow, in particular, there could be references to children and even a place of residence.