Thats certainly an ambitious proposal - LCY/AMS up to 8 times a day - against AFKLM.
It remains to be seen if they operate all the flights, but they will be operating the first flight out and last flight back to and from AMS, both of which will be nearly an hour earlier and later than AFKLM, which is bound to appeal to the business traveller.
I don't suppose that all that many folk going to AMS from LCY really need to interline, or if they want to they will for the most part, only be carrying light luggage for a few nights in Europe, so if Eastern can't get that facility in AMS it won't be the end of the world.
Given their much lower operating costs v the monolith that is AFKLM, they can easily match the fares,even if they were discounted by the opposition.
Hope it goes well for them.