We consider invertible Bloom lookup tables (IBLTs) which are probabilistic data structures that allow to store keyvalue pairs. An IBLT supports insertion and deletion of key-value pairs, as well as the recovery of all key-value pairs that have been inserted, as long as the number of key-value pairs stored in the IBLT does not exceed a certain number. The recovery operation on an IBLT can be represented as a peeling process on a bipartite graph. We present a density evolution analysis of IBLTs which allows to predict the maximum number of key-value pairs that can be inserted in the table so that recovery is still successful with high probability. This analysis holds for arbitrary irregular degree distributions and generalizes results in the literature. We complement our analysis by numerical simulations of our own IBLT design which allows to recover a larger number of key-value pairs as state-of-the-art IBLTs of same size.