Probably not. In therapeutic doses lithium has no psychotropic effects.
“Upon ingestion, lithium becomes widely distributed in the central nervous system and interacts with a number of neurotransmitters and receptors, decreasing norepinephrine release and increasing serotonin synthesis.”
“The most common side effects are an overall dazed feeling and a fine hand tremor. “
And there are different preparations of lithium:
“...used lithium urate, already known to be the most soluble urate compound, and observed that this caused the rodents to be tranquilized.Cade traced the effect to the lithium ion itself. Soon, Cade proposed lithium salts as tranquilizers,... “
“In 2009, Japanese researchers at Oita University reported that low levels of naturally-occurring lithium in drinking water supplies reduced suicide rates. A previous report had found similar data in the American state of Texas. In response, psychiatrist Peter Kramer raised the hypothetical possibility of adding lithium to drinking water”
Note that it is said to have no OBVIOUS psychotropic properties at therapeutic levels. Not ‘no psychotropic properties’ but no OBVIOUS ones. Which accounts for the portion of the linked article that said lithium laced water was also called ‘happy water’. The effects are not obvious enough to disrupt daily functioning but they had an observable effect on ‘happiness’. Or, as a tranquilizer - whichever preparation was selected.