Do lights in a circuit have to be grounded for the whole circuit to be grounded?
If I'm interpreting your drawing correctly, 3 possibilities (all incorrect under current code) may have existed in the past:  


They may have had a 220v line at one time split between 2 cables.  
They had 2 cables but a wire got cut or broken so they used a wire from each of the cables to build a circuit.  
They paralleled wires from 2 cables for higher current capacity.  


I have found all 3 of these in my own 1929 house.

Regardless of which case it is, there's a break in the ground between the breaker panel and the outlet. You'll have to trace the circuit to find the break and correct it.  As Isherwood said, your best solution is to rewire that circuit with a single new grounded cable from the panel out.