Just to be sure: Note that orbitals(*) themselves have neither spin, neither charge. They are not real objects, but theoretical constructs of quantum atom models, that fit well the observations.
Every atom has theoretically infinite number of orbitals ( 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f etc), all but some unoccupied. For most scenarious, it is practical to consider just few highest occupied and few lowest unoccupied orbitals (like 1s, 2s, 2p, 3s, 3p for Li), what may be the reason your chem package provides just few.
Electrons are fermions, so the unpaired $\mathrm{2s}$ electron has the spin 1/2. The spin of a lithium nucleus depends on the isotope. $^6\ce{Li}$ has the spin 1(**), $^7\ce{Li}$ has spin 1/2. The net charge of lithium atom is zero, the charge of the unpaired 2s electron is obviously $-\mathrm{e}$.
Similarly, $\ce{LiH}$ has unlimited number of atomic or molecular orbitals ( depending on the quantum model ), as they are features of quantum models, not real objects. And again, only highest "valence" occupied and few lowest unoccupied ones are worthy to consider. (For $\ce{LiH}$, s and p for atomic ones, $\sigma, \pi $ for molecular ones. )
The orbitals with very high principal quantum number $n$ converge for $\mathrm{n} \rightarrow \infty$ to energetic continuum with very low ionization energy. If occupied by careful excitation, they have very interesting behaviour like effectively disappearing quantization. Such electrons behave like orbitting classically a point-like central charge. See Rydberg atoms for more. They have also ridiculous values of atomic radius, which increases with $n^2$. E.g. $\ce{H}$ with $n=137$ has radius $\pu{1 \mu m}$ and $\ce{K}$ with $n=600$ would have reportedly size $\pu{0.1 mm}$.
(*) Note that the term orbital has 3 major, related but distinguished meanings:
orbital(1) - a wave function as the particular solution of the Schroedinger's quantum wave equation
orbital(2) - a quantum state of an electron(energy, orbital angular momentum, spin angular momentum), belonging to orbital(1)
orbital(3) - a 3D region (or 3D surface/shape), describing the region of significant probability of electron occurance (or its border threshold value), belonging to orbital(1,2)
(**) The only other stable nuclei with spin 1 are $^2\mathrm{H}$ and $^{14}\mathrm{N}$, as odd-odd nuclei are not generally stable, undergoing beta decay to even-even nuclei. The eventual other stable odd-odd nucleus candidate $\ce{^{10}_{5}B}$ does not count, as its spin is 3, not 1.