  Intensity mapping of multiple emission lines is emerging as a new branch to
astronomy, to probe both properties of ionizing sources and the medium between,
in particular the intergalactic medium. For Epoch of Reionization (EoR)
studies, both multi-line experiments and analysis methods are still in their
infancy. Here we explore optimal survey parameters for Ly$\alpha$ (and
H$\alpha$) intensity mapping up to high redshifts of reionization, and
requirements for optimised synergy with 21cm experiments. We investigate line
sensitivity, spectral resolution and detector pixel size requirements for
optimal (high signal-to-noise) mission output. Power and cross-power spectra in
a fiducial setup are derived, as are mock intensity maps. For line power
spectrum measurements a cumulative signal-to-noise of O$\left(10^3 \right)$,
and for respective cross-spectra with SKA 21cm observations of
O$\left(10\right)$ to O$\left(10^2\right)$ are possible per redshift bin around
the midpoint of reionization. These high signal-to-noise tomographic
measurements are in reach for line sensitivities $>8\times
10^{-18}$erg$\,$s$^{-1}$sr$^{-1}$Hz$^{-1}$, spectral resolution $R>250$ and
detector pixel sizes $<2\,$arcsec; all three requirements are met by the
proposed Cosmic Dawn Intensity Mapper (CDIM). For CDIM similar S/N values are
in reach for H$\alpha$. Already the planned NASA mission SPHEREx will detect
during the EoR Ly$\alpha$ autopower and cross power with 21cm, for
sensitivities better than $10^{-18}$erg$\,$s$^{-1}$sr$^{-1}$Hz$^{-1}$ in a
moderate 21cm foreground scenario (better than
$10^{-17}$erg$\,$s$^{-1}$sr$^{-1}$Hz$^{-1}$ in an optimistic scenario). We
advocate for IR missions in flavor of CDIM for a leap in IM and finish by
providing a cookbook for successful multi-line IM during the EoR.
