As
@sregan pointed out... I wouldn't be sure that the hair test is that significant.
I am not an expert but I wonder how accurate can be the hair mineral content in representing the status of your body tissues.
Hair can be very different for different people, some have strong hair, other much weaker and their color and type influences the minerals they retain. I do a hair test every year, mostly to check heavy metals such as mercury. I am not sure it's 100% accurate, but mercury is not supposed to be in our bodies (in an ideal world) so if it's there it must be because of the diet, amalgams etc...
Additionally it sounds a bit strange that no effect seems to be found after 1 year of supplementation. Unless you have gut malabsorption issues the mineral should be in your system.
Did you have any positive effects from taking the mineral? If not maybe you could try a higher dose, Lithium orotate is considered safe in the range of 5-10mg / day although I am not sure if there's any literature about long term supplementation.
It would be interesting to know if there are labs that can measure intracellular lithium as they do for zinc, magnesium etc...