Colour in aqueous solutions of transition and inner transition elements is primarily due to electron transitions (d-d or f-f transitions) which require the presence of unpaired electrons in the d or f orbitals.

1. $La^{3+} (Z=57)$: Electronic configuration is $[Xe] 4f^0$. With an empty f-orbital, there are no unpaired electrons. It is colourless .
2. $Ti^{3+} (Z=22)$: Electronic configuration is $[Ar] 3d^1$. It has one unpaired electron in the 3d orbital. This electron can undergo d-d transition, absorbing yellow-green light and transmitting purple/violet colour .
3. $Lu^{3+} (Z=71)$: Electronic configuration is $[Xe] 4f^{14}$. The f-orbital is completely filled. With no unpaired electrons, it is colourless .
4. $Sc^{3+} (Z=21)$: Electronic configuration is $[Ar] 3d^0$. With an empty d-orbital, it is colourless .