  For a division ring $\mathbb F$, the polynomials $f\in\mathbb F$ can be
evaluated "on the left" and "on the right" giving rise to left and right
Lagrange interpolation problems. The problems containig interpolation
conditions of the same type were considered in \cite{lam1} where the
solvability criterion was given in terms of polynomial independence of
interpolation nodes. We establish the solvability criterion and describe all
solutions of low degree (less than the number of interpolation conditions
imposed) for the problem containing both "left" and "right" conditions.
