Is it possible for me to catch a 2pm flight from Zurich on June 27?
Yes. Use the SBB website. Input:
From Lauterbrunnen
To Zurich Airport
Date Tu, 27.06.17 (use calender function)
Time 11:00 checking the "Arrival" button.
You will get four train itineraries starting with
Depart 6:33/Arrive 9:19 thourgh
Depart 8:03/Arrive 10:42
The last (Depart 8:03/Arrive 10:42) gives you more than 3 hours before flight on a Tuesday (mid-week). Swiss Air (D0n't know about the Icelandic check-in) has a lot of flights departing mid-day but more than 3 hours should be fine.
Lauterbrunnen dep 08:03
Regio 128
Direction: Interlaken Ost
Interlaken Ost arr 08:24
Change
Interlaken Ost dep 08:30
InterCity 1062
Direction: Basel SBB
Bistro Minibar or catering zone Family Coach with play area BZ RZ Reservation possible
Bern arr 09:23
Change
Bern dep 09:32
InterCity 711
Direction: St. Gallen
Restaurant Minibar or catering zone Family Coach with play area BZ RZ Reservation possible
Zürich Flughafen arr 10:42
You my feel more comfortable if you buy your ticket from a staffed SBB counter a day ahead and they can reassure you of the schedule.