  We derive stationary and fixation times for the multi-type
$\Lambda$-Wright-Fisher process with and without the classic linear drift that
models mutations. Our method relies on a grand coupling of the process realized
through the so-called lookdown-construction. A well-known process embedded in
this construction is the fixation line. We generalise the process to our setup
and make use of the associated explosion times to obtain a representation of
the fixation and stationary times in terms of the waiting time in a coupon
collector problem.
