To have a phase diagram with 1 eutectic point, the two compounds must be miscible in the liquid state (should be fulfilled for your example, because both compounds are hydrophilic) and immiscible in the solid state (likely for your example). You have to make sure, however, that the two compounds do not form solid adducts or chemical reaction products, because that might produce other phase diagram types. In your example, glycerol and lactic acid might form esters. Then one has to know to which extent esters form and what their melting points are.

thanks so much!!