SQL Server 2017

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CREATE TABLE mytable(
   Inst        INTEGER  NOT NULL 
  ,Acct        INTEGER  NOT NULL
  ,First       VARCHAR(6) NOT NULL
  ,MI          VARCHAR(1)
  ,Last        VARCHAR(6) NOT NULL
  ,Activty     VARCHAR(6) NOT NULL
  ,ActivtyDate VARCHAR(23) NOT NULL
);
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'EDWARD',NULL,'BICKLE','OptIn','2019-05-25 12:02:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'EDWARD',NULL,'BICKLE','OptIn','2019-05-25 12:37:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'KIM',NULL,'BICKLE','OptIn','2019-06-17 08:43:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'EDWARD',NULL,'BICKLE','OptOut','2019-06-20 11:57:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'EDWARD',NULL,'BICKLE','OptOut','2019-06-20 23:10:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'EDWARD',NULL,'BICKLE','OptOut','2019-06-21 08:46:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'EDWARD',NULL,'BICKLE','OptIn','2019-06-27 10:34:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'EDWARD',NULL,'BICKLE','OptOut','2019-06-27 10:35:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'EDWARD',NULL,'BICKLE','OptOut','2019-06-27 23:04:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'KIM',NULL,'BICKLE','OptIn','2019-07-02 11:35:42.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'EDWARD',NULL,'BICKLE','OptOut','2019-07-05 15:04:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'EDWARD',NULL,'BICKLE','OptIn','2019-07-06 07:57:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'EDWARD',NULL,'BICKLE','OptIn','2019-07-06 08:16:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (001,00000000001111111,'EDWARD',NULL,'BICKLE','OptIn','2019-07-09 08:17:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (000,00000000002222222,'DAWN','M','ADAMS','OptOut','2019-03-03 20:51:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (000,00000000002222222,'DAWN','M','ADAMS','OptOut','2019-03-03 20:51:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (000,00000000002222222,'DAWN','M','ADAMS','OptIn','2019-03-08 19:10:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (000,00000000002222222,'DAWN','M','ADAMS','OptIn','2019-03-16 06:34:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (000,00000000002222222,'DAWN','M','ADAMS','OptOut','2019-03-18 16:21:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (000,00000000002222222,'DAWN','M','ADAMS','OptIn','2019-03-21 16:38:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (000,00000000002222222,'DAWN','M','ADAMS','OptOut','2019-03-22 05:26:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (000,00000000002222222,'DAWN','M','ADAMS','OptIn','2019-04-01 15:39:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (000,00000000002222222,'DAWN','M','ADAMS','OptOut','2019-04-02 04:06:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (000,00000000002222222,'DAWN','M','ADAMS','OptIn','2019-04-06 11:53:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (000,00000000002222222,'DAWN','M','ADAMS','OptOut','2019-04-09 12:51:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (000,00000000002222222,'DAWN','M','ADAMS','OptOut','2019-04-20 15:21:00.000');
INSERT INTO mytable(Inst,Acct,First,MI,Last,Activty,ActivtyDate) VALUES (000,00000000002222222,'DAWN','M','ADAMS','OptIn','2019-04-20 15:21:00.000');

27 rows affected

Inst	Acct	First	MI	Last	Activty	ActivtyDate	lag_activity
1	1111111	EDWARD	null	BICKLE	OptIn	2019-05-25 12:02:00.000	null
1	1111111	EDWARD	null	BICKLE	OptOut	2019-06-20 11:57:00.000	OptIn
1	1111111	EDWARD	null	BICKLE	OptIn	2019-06-27 10:34:00.000	OptOut
1	1111111	EDWARD	null	BICKLE	OptOut	2019-06-27 10:35:00.000	OptIn
1	1111111	KIM	null	BICKLE	OptIn	2019-07-02 11:35:42.000	OptOut
1	1111111	EDWARD	null	BICKLE	OptOut	2019-07-05 15:04:00.000	OptIn
1	1111111	EDWARD	null	BICKLE	OptIn	2019-07-06 07:57:00.000	OptOut
0	2222222	DAWN	M	ADAMS	OptOut	2019-03-03 20:51:00.000	null
0	2222222	DAWN	M	ADAMS	OptIn	2019-03-08 19:10:00.000	OptOut
0	2222222	DAWN	M	ADAMS	OptOut	2019-03-18 16:21:00.000	OptIn
0	2222222	DAWN	M	ADAMS	OptIn	2019-03-21 16:38:00.000	OptOut
0	2222222	DAWN	M	ADAMS	OptOut	2019-03-22 05:26:00.000	OptIn
0	2222222	DAWN	M	ADAMS	OptIn	2019-04-01 15:39:00.000	OptOut
0	2222222	DAWN	M	ADAMS	OptOut	2019-04-02 04:06:00.000	OptIn
0	2222222	DAWN	M	ADAMS	OptIn	2019-04-06 11:53:00.000	OptOut
0	2222222	DAWN	M	ADAMS	OptOut	2019-04-09 12:51:00.000	OptIn
0	2222222	DAWN	M	ADAMS	OptIn	2019-04-20 15:21:00.000	OptOut