  We study the asymptotic distribution of roots of Lommel polynomials as
polynomials of the order with a variable and purely imaginary argument. The
roots are complex and accumulate on certain curves in the complex plane. We
prove existence of the weak limit of corresponding root-counting measures and
deduce formulas for the supporting curves and density. The obtained result
represents a solvable example of a more general problem which is still open.
Numerical illustrations of the main result are also involved.
