They actually have nearly opposite goals. The fusion blanket is supposed to transmute lithium to tritium [0] (create more fusion fuel), so it has capture as many neutrons as possible. The fission-reactor coolant is supposed to be transparent -- to capture as few neutrons as possible. Both of them need isotopic separation of lithium to be practical. But in opposite directions. ARC's FLiBe needs to be Li-6 enriched, and MSR needs to be Li-6 depleted.

The MSRE fuel used 99.993% Li-7 (your link), and the ARC blanket is 90% Li-6 (arXiv paper).

[0] https://www.iter.org/mach/tritiumbreeding