In lithium the 2p orbitals have a higher energy than a 2s orbital, why?

Answer 1

the 2p orbital is further away from the nucleus

Answer 2

To "visualise" both the situation & this "energy", notice also that what is being discussed is the potential charge within a dipole. The "measure of energy" is that required to "stretch" the dipole to a greater distance.

Notice within the "lattice structure" that is a {Solid} this energy is even labelled as being the Zero Point Energy of that (quantum) structure as it is that "Energy" still present when that structure is presented at "Absolute Zero".

It is this "ZPE" that enables the disassociated situation of those Electrons that constitute the Lattice Structure of the {Solid} to continue at "Absolute Zero", else instead of "freezing" the {Solid} would dis-integrate into the constituent molecules &/or atoms, that would scavenge those Electrons in a short term "quantum tug-o-war" within a {temporarily) ionized "low energy plasma" cloud.

Yours, Peter K. Anderson a.k.a. Hartlod(TM)