| Summary: | In view of the future plans to measure the Lamb shift in muonic Lithium atoms
we address the microscopic theory of the $\mu$-$^6$Li$^{2+}$ and
$\mu$-$^7$Li$^{2+}$ systems. The goal of the CREMA collaboration is to measure
the Lamb shift to extract the charge radius with high precision and compare it
to electron scattering data or atomic spectroscopy to see if interesting
puzzles, such as the proton and deuteron radius puzzles, arise. For this
experiment to be successful, theoretical information on the nuclear structure
corrections to the Lamb shift is needed. For $\mu$-$^6$Li$^{2+}$ and
$\mu$-$^7$Li$^{2+}$ there exist only estimates of nuclear structure corrections
based on experimental data that suffer from very large uncertainties. We
present the first steps towards an ab initio computation of these quantities
using few-body techniques.
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