Why the solubility of sodium chloride in water increase with rise in temperature while that of lithium carbonate decreases
The dissolution of lithium carbonate in water is exothermic. Adding further heat will drive the reaction backwards according to Le Chatliers principle about which you will learn in 11th standard
What you refer to, the decreased in a solid's solubility in a liquid with increased temperature, is frequently called retrograde or inverse solubility, and occurs when the dissolution of the solute is exothermic.
The explanation for this can be viewed as a manifestation of Le Chatelier's principle. Essentially, since evolved heat can be viewed as a product of an exothermic reaction, the addition of more heat (e.g. a higher temperature) is equivalent to adding a product to the product side of the chemical equation for dissolution, driving the equilibrium back toward the reactants, in this case toward the undissolved compound.