Is lithium bicarbonate an aqueous solution of lithium carbonate?
Lithium bicarbonate solution is something like a lithium carbonate solution in the sense that precipitation would produce the carbonate instead of the bicarbonate.  But what is in solution is mostly lithium and bicarbonate ions.  Precipitation is accompanied by a reaction in which the highly polarizing lithium ions react with bicarbonate:

$2\ce {Li+}+2\ce {HCO_3-}\rightarrow \ce {Li2CO_3}(s)+\ce {H2O}+\ce {CO2}$

Other alkali metals give less polarizing ions and do not react in the same way; they just precipitate the bicarbonate salt.