Would the enthalpy of atomisation for potassium be more endothermic than that of lithium?
No the enthalpy of atomisation of K would be less than Li. It depends on the forces holding the atoms together in the standard state, which in both cases is solid metal. As both Li and K have one electron in the outer shell they contribute this to the delocalised electrons which then attract the positive ions in the metallic lattice. As K is a larger atom the electrons are further from the nuclei and hence the forces of attraction are lower and the metallic bonds weaker. Hence the enthalpy of atomisation of K is lower than Li.