What's the type of bonding in La@C60?
That the question says: "Without any 'binding' forces, the atom couldn't be possibly trapped inside the fullerene", shows you are misunderstanding fullerenes.  

Atoms such as Helium and $H_2$ can be confined within the interior of the fullerene.  

There are even reports of extraterrestrial helium trapped in fullerenes during astroid or comet impact.

The helium can move around within the fullerene.  It is sterically confined rather than bonded.  

In the case of La, the metal ion does not remain neutral, but loses about 3 electron to the fullerene.  So, in addition to being sterically confined in the cage, there is the interaction between postively and negatively charged species.  

As calculated in a later article Computed Structure and Energetics of
La@C60 International Journal of Quantum Chemistry, Vol 104, 272–277 (2005), the La has a charge of somewhere betwen 2+ and 3+.  In the lowest energy state, the La is off-center with respect to the fullerene, located between the center and the center of a hexagon face.  Also, the fullerene cage is distorted from icosahedral by Jahn-Teller distortion.  

The La ion is located 2.62 Angstroms from the nearest carbon atom (4.6 Angstroms from the furthest), when at the potential miniumun, but is expected to move within the fullerene unless the temperature is very low.  The reference also says "there is obviously a relatively large negative charge on some carbon atoms of the cage", without specifying how this charge is distributed.  

Overall I would say, whereas in the case of helium and dihydrogen being confined in the fullerene is completely because of van der Waal repulsive force of avoiding the walls, in the case of La, there is attractive electrostatic force (ionic interaction) between the La3+ and negatively charged carbon atoms.  

See also Theoretical investigation of structural and thermodynamic properties
of lanthanum carbides LaCn (n = 2–6) which finds strong ionic interactions between La and Cn due to charge transfer.