No, the lid should not be used during the boil stage for a number of reasons, including:
The boil will seem excessive as residual heat is not allowed to escape resulting in a vigorous boil and in extreme cases a boil over.
Our recipe calculator takes into account the boil off rate of the wort, that is the amount of steam that is allowed to escape during the boil. If the lid is used the steam is not allowed to escape at the same rate and as such the final volume and OG will not match the calculated values.
While boiling wort a substance known as DMS is evaporated, DMS causes a creamed corn/cooked vegetable off flavour in beer, if the boiler is covered the DMS cannot be evaporated and will fall back into the wort resulting in an off tasting end product.