I was not so much suggesting that the Brtish GP would influence the date of the LM race, more the fact that any F1 race might.
I know there is no connection between LM teams and F1 teams these days, but the ACO do appear to be more co-operative with the FIA these days.
Thus, I seem to recall there was some discussion in the motorsport mags / forums last year, about the ACO and the FIA making an effort to not have an F1 snooze fest and the LM24 happening on the same weekend.
Something to do with maximising TV and spectator coverage / exposure.