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db<>fiddle
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with data as (
select 1 CID, TO_DATE('2020-05-29','YYYY-MM-DD') IN_DATE from dual union all
select 1, TO_DATE('2020-06-10','YYYY-MM-DD') from dual union all
select 1, TO_DATE('2020-06-21','YYYY-MM-DD') from dual union all
select 1, TO_DATE('2020-07-08','YYYY-MM-DD') from dual union all
select 1, TO_DATE('2020-08-11','YYYY-MM-DD') from dual union all
select 2, TO_DATE('2020-05-05','YYYY-MM-DD') from dual union all
select 2, TO_DATE('2020-05-03','YYYY-MM-DD') from dual union all
select 2, TO_DATE('2020-06-01','YYYY-MM-DD') from dual union all
select 2, TO_DATE('2020-06-02','YYYY-MM-DD') from dual union all
select 2, TO_DATE('2020-06-03','YYYY-MM-DD') from dual
)
select CID,
to_char(TO_DATE(IN_DATE), 'YYYY-MM-DD') IN_DATE,
TO_CHAR(MAX(IN_DATE) OVER (PARTITION BY CID
ORDER BY TRUNC(IN_DATE, 'MON')
RANGE BETWEEN UNBOUNDED PRECEDING AND INTERVAL '1' MONTH PRECEDING
),
'YYYY-MM') as LAG
from data
CID IN_DATE LAG
1 2020-05-29 null
1 2020-06-10 2020-05
1 2020-06-21 2020-05
1 2020-07-08 2020-06
1 2020-08-11 2020-07
2 2020-05-05 null
2 2020-05-03 null
2 2020-06-01 2020-05
2 2020-06-02 2020-05
2 2020-06-03 2020-05