The ions present in the original solution are:
\[
\boxed{\mathrm{Ca^{2+}} \text{ and } \mathrm{Co^{2+}}}
\]
Net ionic equation for the formation of the precipitate with lithium sulfate:
\[
\boxed{\mathrm{Ca^{2+}(aq) + SO_4^{2-}(aq) \rightarrow CaSO_4(s)}}
\]
Net ionic equation for the formation of the precipitate with lithium phosphate:
\[
\boxed{3\mathrm{Co^{2+}(aq) + 2PO_4^{3-}(aq) \rightarrow Co_3(PO_4)_2(s)}}
\]