If you heat aqueous hydrochloric acid up to boiling, you're going to drive all the acid off, fast. There shouldn't be any need for heat at all. The oxidation of lithium by HCl will take place at room temp (quite vigorously actually, you should keep the solution cooled if anything). This will yield VERY soluble lithium chloride. To this solution, you add enough sodium carbonate to both neutralize any excess acid and displace chloride to form lithium carbonate and sodium chloride. Lithium carbonate is sparingly soluble in water while sodium chloride is very soluble. Heat the solution at this point to make sure all sodium chloride dissolves, then filter hot to collect the lithium carbonate.