  We investigate the behaviour of an establishing mutation which is subject to
rapidly fluctuating selection under the Lambda-Fleming-Viot model and show that
under a suitable scaling it converges to the Feller diffusion in a random
environment. We then extend to a population that is distributed across a
spatial continuum. In this setting the scaling limit is the SuperBrownian
motion in a random environment.The scaling results for the behaviour of the
rare allele are achieved via particle representations which belong to the
family of `lookdown constructions'. This generalises the results obtained for
the neutral version of the model by Chetwynd-Diggle and Etheridge (2018), which
was proved using a duality argument. To our knowledge this is the first
instance of the application of the lookdown approach in which other techniques
seem unavailable.
