I thought I would add to his post from my experience in this field.
Accurate pH can only be checked at sampling time. even in tightly sealed containers, there may be some pH change in transit. This is particularly true in low buffered waters(low alkalinity and conductivity waters). CO2 from the air can be absorbed and lower pH, and CO2 can be lost to the air raising pH. I would trust the reading you took at sampling over the reading from the LSU testing on such low buffered water.
When analyzing the water results, you need to know if the results are reported as ion or as CaCO3 equivalents. Most water samples are reported as calcium carbonate; i.e. calcium 40 ppm as CaCO3. The same goes for alkalinity. This is done to get everything reported in the same terms for ionic balance. If this report is as CaCO3 equivalent, you have extremely low calcium hardness and alkalinity. If as ion, then not so much.
I agree that adding lime seems to be in order.
