...but why cannot the southern be used for departures in LVP?
The same reason they don't clear you for T/O on RWY12R when there is an aircraft between 200-1000' on final approach for 12L. Through either ignorance or more probably to save money the runways were built too close together for unrestricted parallel operations as at proper airports.
It is slightly less of an issue on the RWY30s in good weather as their respective thresholds are further apart. This is why RWYs 30L & 30R are used 90% of the time, they can get more movements per hour because they are less restricted with simultaneous T/Os and LDGs using 30 than 12.