There is a whole thesis to be written just on this small topic. I would likely not take a job for The Warehouse (or for that matter, shop there), yet I recognise that the funding comes from Stephen Tindall as a generous philanthropist. Is that separation enough? Is it OK to work on LAWA as it is one or two steps removed?
I would actually be a hypocrite if I said it was not OK. When I worked for Surf Life Saving New Zealand, The Warehouse donated directly to the organisation and though I was not thrilled about it, I did not consider resigning.
There is also a double standard here. I recognise that as an employee of a company, it would not be clear where that company invested or who they supplied, so this is something of a privileged problem to have.
The way donations are perceived in the UK versus New Zealand are very different. In the UK, a charity taking money from a company (or an individual closely associated with a company) expects to get questioned on the ethics of this in the press. In New Zealand, much less so. At SLSNZ, I said in jest (though I was at least half serious) that I would resign if the organisation took money from KFC (how can a sporting organisation accept money from a junk food peddler?). After I had moved on, it actually happened, and not a murmur accompanied it.
The Warehouse is something of a national institution, and I doubt most New Zealanders consider it at all unethical so there will be no backlash against LAWA from the public. But again this highlights the need for a designer to consider their own personal position.