Activity of NaCl aqueous solution at high ionic strengths: Common-ion effect

Is there any theoretical way to estimate the activity of $\ce{NaCl}$ at high ionic strengths in water and that in $\pu{7 M}$ $\ce{NaCl}$ solution? This question is based on whether solubility of $\ce{NaCl}$ in $\pu{7 M}$ $\ce{LiCl}$ solution should decrease. Solubility of $\ce{Na+}$ in $\ce{LiCl}$ solution can be approximated to 


$$
[\ce{Na+}]=\frac{(K\_\mathrm{sp})\_{\ce{NaCl}}}{m\_{\ce{LiCl}}}
$$


We have, however, assumed that both $\ce{NaCl}$ (and $\ce{LiCl}$) are in their unit activities, which is not true. How to get conservative estimates for $a\_{\ce{LiCl}}$ and $a\_{\ce{NaCl}}$ at high ionic strengths, say $\pu{7 M}$? 


