In a water molecule, two hydrogen atoms bind to one oxygen atom. How many lone pairs of electrons will be shown around each hydrogen atom in the Lewis structure of water?

Zero lone pairs of electrons, because the water molecule is a bent shape, meaning that the atom in the center has the lone pairs of electrons which is Oxygen, not Hydrogen.

There are no lone pair of electrons shown around the hydrogen atoms, rather there are 2 lone election pairs present around the central atom in this Lewis structure and that is Oxygen. Hydrogen only has bonding electrons, and it requires 2 electrons per hydrogen to achieve stability and have a full valence electron shell.