  To use strongly lensed Type Ia supernovae (LSNe Ia) for cosmology, a
time-delay measurement between the multiple supernova (SN) images is necessary.
The sharp rise and decline of SN Ia light curves make them promising for
measuring time delays, but microlensing can distort these light curves and
therefore add large uncertainties to the measurements. An alternative approach
is to use color curves where uncertainties due to microlensing are
significantly reduced for a certain period of time known as the achromatic
phase. In this work, we investigate in detail the achromatic phase, testing
four different SN Ia models with various microlensing configurations. We find
on average an achromatic phase of around three rest-frame weeks or longer for
most color curves but the spread in the duration of the achromatic phase (due
to different microlensing maps and filter combinations) is quite large and an
achromatic phase of just a few days is also possible. Furthermore, the
achromatic phase is longer for smoother microlensing maps, lower
macro-magnifications and larger mean Einstein radii of microlenses. From our
investigations, we do not find a strong dependency on the model or on
asymmetries in the SN ejecta. Further, we find that three independent LSST
color curves exhibit features such as extreme points or turning points within
the achromatic phase, which make them promising for time-delay measurements.
These curves contain combinations of rest-frame bands $u$, $g$, $r$, and $i$
and to observe them for typical LSN Ia redshifts, it would be ideal to cover
(observer-frame) filters $r$, $i$, $z$, $y$, $J$, and $H$.
