  L\"uroth series, like regular continued fractions, provide an interesting
identification of real numbers with infinite sequences of integers. These
sequences give deep arithmetic and measure-theoretic properties of subsets of
numbers according to their growth. Although different, regular continued
fractions and L\"uroth series share several properties. In this paper, we
explore one similarity by estimating the Hausdorff dimension of subsets of real
numbers whose L\"uroth expansion grows at a definite rate. This is an extension
of a result of Y. Sun and J. Wu to the context of L\"uroth series. It was
recently shown by Y. Feng, B. Tan, and Q.-L. Zhou that the lower bound in our
main theorem is actually an equality.
