Can two lone pairs in different orbitals make a chiral centre? Is it possible that if the two lone pairs in a molecule occupy different orbitals, then could this make the molecule chiral? What I mean is, suppose a carbon atom is attached to two different atoms and has two lone pairs in different orbitals, then could the carbon atom be considered chiral?
Chirality refers only to the positions of the nuclei. So, if we have the situation you described where one Carbon is bonded to two other atoms (e.g. CX$_2$ or CXY) it can never be chiral. (i.e. a three atom molecule can always be superimposed on its mirror image by a single rotation)

Now, why don't we consider the atomic and hybrid orbitals  populations when assigning chirality? This comes down to the fact that the atomic and hybrid orbitals are just a helpful tool for rationalizing/predicting the structure and reactivity, but they are not representations of the actual wavefunction. The true wavefunction is defined by a set of ''molecular orbitals.'' These orbitals always have the same symmetry group as the nuclear coordinates. In this case, there is a reflection through the plane defined by the three atoms (some jargon: this is called the C$_{s}$ symmetry point group). So if the nuclear positions are non-chiral, so is the wavefunction. 

(More on chirality and symmetry: http://symmetry.otterbein.edu/tutorial/applications.html)