Surely it isn't about EI, it is all about strategy for LH and Star at Heathrow.

If LH can persuade EI into Star (or force it to do so by purchasing a stake) then it can free up more than a dozen slots by handing the Belfast and Dublin routes to EI. This would then give LH freedom to choose between building the BD position at LHR, building the position of other Star carriers at LHR (as is currently the trend), selling the newly-free slots in a fire-sale to make some cash, or cherry-picking what's left of BD before selling the remainder (in whole or in parts) along with the slots (in whole or in part).