  We investigate a recent claim that observed galaxy clusters produce an order
of magnitude more galaxy-galaxy strong lensing (GGSL) than simulated clusters
in a LCDM cosmology. We take galaxy clusters from the C-EAGLE hydrodynamical
simulations and calculate the expected amount of GGSL for sources placed behind
the clusters at different redshifts. The probability of a source lensed by one
of the most massive C-EAGLE clusters being multiply imaged by an individual
cluster member is in good agreement with that inferred for observed clusters.
We show that numerically converged results for the GGSL probability require
higher resolution simulations than had been used previously. On top of this,
different galaxy formation models predict cluster substructures with different
central densities, such that the GGSL probabilities in LCDM cannot yet be
robustly predicted. Overall, we find that galaxy-galaxy strong lensing within
clusters is not currently in tension with the LCDM cosmological model.
