Is having a lone pair sufficient and necessary for a Lewis base? What about empty orbitals and Lewis acids?
No, not every molecule that has a valence lone pair is automatically a Lewis base.

For example, tin forms divalent salts such as $\ce{SnCl2}$ wherein tin is in the $\mathrm{+II}$ oxidation state and thus its electronic configuration is $\ce{[Kr]}\ \mathrm{4d^{10}\,5s^2\,5p^0}$. Even if we say that the d-electrons are not really valence electrons, since they are not really chemically accessable, you cannot deny that tin(II) has a lone pair in its 5s orbital. However, this lone pair does not exhibit Lewis basic properties; instead, tin(II) functions as a Lewis acid. The reason for that is the spherical symmetry of the s-orbital along with its notable dispersion, which means it cannot be reasonably donated in a Lewis-basic matter.

Note that the lone pair is accessable chemically: tin(II) can be oxidised to tin(IV) e.g. by $\ce{HgCl2}$.



A somewhat similar (but much more questionable!) case can be made for electron sextets and Lewis acids. NHCs are a pretty common substance class. The most generic structure is that of imidazole, but with both nitrogens substituted so that one of them bears a positive charge (the one with a double bond to the carbon sandwiched between the two). If a base is added to remove that sandwiched carbon’s proton, a carbene is generated in which said carbon is only bonded to the nitrogen, has an $\mathrm{sp^2}$ configured lone pair and is considered to have an empty $\mathrm{p}$ orbital. However, this carbene is nucleophilic, which is why they are also called nucleophilic heterocyclic carbenes. They react as Lewis bases with metal centres; the second generation of Grubbs’ metathesis catalysts made use of NHCs.

Of course, it is slightly debatable whether the p-orbital on that NHC carbon is truly empty. One could argue that significant electron pair donation from both nitrogens should happen.

(As a side note: radicals, while not having full octets, are typically never considered Lewis acids — but then, their orbital is already occupied by a single electron, so they don’t have an empty orbital that would make them a potential Lewis acid, anyway. Thus, your question should better be worded differently to explicitly exclude radicals.