There will be no trains on this date from Tel Aviv to the Airport, there will be free of charge shuttles between Tel Aviv Savidor and Lod stations and the Airport.
The Hebrew site has an announcement about the shutdown, an English translation appeared later, linked from the “Updates” section. The announcement has the times of the shuttles, copied below. However, in practice, at least from Tel Aviv to the airport, the shuttle leaves when the driver thinks there are enough passengers, rather than at set times. This seems to amount in a little more than the advertised frequency of one bus per hour, but don't plan any tight connection.
Friday the 15th:
Tel Aviv to Airport: 00:42, 01:00, 01:42, 02:42, 03:42, 04:42, 05:45, 06:45, 07:45, 08:45, 09:45, 11:45, 12:45, 13:45, 14:45, 15:45, 16:45, 17:10
Airport to Tel Aviv: 00:53, 01:53, 02:53, 03:53, 04:53, 05:38, 06:38, 07:38, 08:38, 09:38, 10:38, 11:38, 12:38, 13:38, 14:38, 15:38, 16:38
Lod to Airport: 07:30, 08:30, 09:30, 10:30, 11:30, 12:30, 13:30, 14:30, 15:30, 16:30
Airport to Lod: 07:05, 08:05, 09:05, 10:05, 11:05, 12:05, 13:05, 14:05, 15:05, 16:05
Saturday the 16th - Sunday the 17th:
Tel Aviv to Airport: 22:27, 23:27, 00:06, 01:42, 02:42, 03:42, 04:42
Airport to Tel Aviv: 21:38, 22:38, 23:35, 00:53, 01:53, 02:53, 03:53, 04:53
Lod to Airport: 21:50, 22:00, 23:00
Airport to Lod: 22:15, 22:55, 23:55
I have contacted Israel Railways through the chat on their site and got the reply:
מה 14-17.9 תיהיה סגירה של תחנת ת"א ההגנה לצורך עבודה על המסילות- מלבד מסילות 4-5. לכן, לא יהיו רכבת כלל מת"א לנתב"ג. יהיו שאטלים מת"א סבידור לנתב"ג. המידע על השאטלים יפורסם בהמשך
Which translates to:
During 14-17/9 Tel Aviv Hahagana station will be closed for maintenance of the rails, except for rail 4-5, because of this, there will be no trains from Tel Aviv to Ben Gurion Airport. There will be shuttles from Tel Aviv Savidor.
Information about the shuttles will be published later.
Tel Aviv Savidor is also called Tel Aviv Center and Tel Aviv Arlozorov