  It is common practice in cosmology to model large-scale structure observables
as lognormal random fields, and this approach has been successfully applied in
the past to the matter density and weak lensing convergence fields separately.
We argue that this approach has fundamental limitations which prevent its use
for jointly modelling these two fields since the lognormal distribution's shape
can prevent certain correlations to be attainable. Given the need of ongoing
and future large-scale structure surveys for fast joint simulations of
clustering and weak lensing, we propose two ways of overcoming these
limitations. The first approach slightly distorts the power spectra of the
fields using one of two algorithms that minimises either the absolute or the
fractional distortions. The second one is by obtaining more accurate
convergence marginal distributions, for which we provide a fitting function, by
integrating the lognormal density along the line of sight. The latter approach
also provides a way to determine directly from theory the skewness of the
convergence distribution and, therefore, the parameters for a lognormal fit. We
present the public code Full-sky Lognormal Astro-fields Simulation Kit (FLASK)
which can make tomographic realisations on the sphere of an arbitrary number of
correlated lognormal or Gaussian random fields by applying either of the two
proposed solutions, and show that it can create joint simulations of clustering
and lensing with sub-per-cent accuracy over relevant angular scales and
redshift ranges.
