  We produce chain-level generators of the virtual Lee complex $ Kh ' (V ) $
and use them to convert the computable bounds on the Rasmussen invariant of
classical knots due to Kawamura and Lobb into bounds on the virtual Rasmussen
invariant as defined by Dye, Kaestner, and Kauffman. We also exhibit a class of
diagrams for which the bounds are tight. In addition, we use the chain-level
generators to show that the virtual Rasmussen invariant is additive with
respect to connect sum.
