I'm not sure how this would work, MarkD; for a start, only airlines can currently hold slots. That rule may change, but for the moment that's the way it is.
The slot issue is one of the issues being focused upon by the government and I am sure that if a BA bid were to get anywhere, rock solid assurances would need to be sought about the EI slots at LHR.
As for routes to Asia, I would have thought that one of the main objectives would be to reduce the reliance on LHR altogether; leasing slots to other carriers would probably not work. They would probably want them to increase their own slots and furthermore, is it actually in Ireland's interests to have most of the capacity on flights to Ireland taken up by UK bound pax.
The issue of EI's plan to develop long haul, low cost routes may be one which gives BA cause for concern. However, we could discuss this extensively, which takes us away from the crucial point: what could BA actually bring to EI? Could it invest money, in the long term. Would it, even if it could? Remember that the march of low cost carriers like EZY and of course RYR, is continuing and I think BA's resources may yet be needed for its own survival, rather than EI's. I just don't see BA as a natural partner for EI and I am uneasy about its intentions for the airline.