Would be kinda pointless to write down the maths, even I only linked to it, typing it out here would be extremely laborious.
Its quite hard to get the full details of Lerners model for Li when his
first publication on it is missing the page after where he says
"The generation of Lithium, Beryllium and Boron also by cosmic ray interactions depends on relatively tiny [....]"
Then theres a missing page. Then the conclusion.

I've definitely read it before as I remember some of the particle production model he proposed. Its related very closely to the Deuterium model, I remember that much.
"Deuterium is produced by cosmic rays in the reaction p + p —> d + π , which has a cross section of 3.3 mb for energies around 1 GeV"
"Deuterium production by the p + p —> d + π reaction has been predicted by plasma theory to yield abundances of the order of 2.2x10-5[8]. While more precise calculations will have to be done to improve this figure and to define the range of values that are likely, it is notable that this prediction was made in 1989, at a time when no observations of high redshift D was available and the consensus values for primordial D from Big Bang theory were 3-4 times higher. Yet this predicted value lies within the range of observed high-z D values, although somewhat below the average D values.
In its present form, the plasma-stellar theory of light elements does not give a prediction for the absolute abundance of 7Li. The observed low and variable abundances of cosmic -ray spallation products of C, N, and O, which are 9Be and 11B in old stars, indicates that 7Li was probably formed by He-He fusion in the interstellar medium, but more modeling will be needed to develop concrete predictions."
So, looks like maybe PC prediction for Li abundances are probably as bad as the Big Bangs predictions.