Is lanthanum a lanthanoid? Is lanthanum classified as lanthanoids? If yes, then can somebody explain in detail why La has 6s2 5d1 as its electron configuration and Ce has 6s2 4f1 5d1?
Yes, Lanthanum is classified as a lanthanide although it does not have any electrons in its f orbital. 

La does not obey the general rule of lanthanides ([Xe]4f^n 6s^2), but is included in this group due to its characteristics (particularly trivalency) being in accordance with the rest of the group. Such as its atomic radius &amp; ionisation energies.

Ce is another exception to the rule (as are Ga &amp; Lu). It ought to be [Xe] 4f^2 6s^2, but the effective nuclear charge, which is still relatively small, is not great enough for f-orbital contraction to be sufficient for 2e in the f orbital. Thus the energy required to fill the f orbitals with 2e is still greater than the energy required to fill the d orbitals. 
That being said, it is equally as difficult to fill the 5d orbitals with both electrons, as the f orbital contraction has lowered the energy required enough such that 1 electron can occupy the f orbitals and the other can occupy the d orbitals. 

I understand if this isn't the exact answer you are looking for as many areas of periodicity have discrepancies, but reasons can essentially be derived back to a balance between the stability of the species &amp; the energetics arising from the occupation of the electron in available orbitals.