My personal preferred solution for this type of exercise is to apply the required previous date to the current row and then use it to join on, I find this makes the intent more obvious:

select t.Id, t.Rec, t.Date, pt.Rec Previous_Rec, pt.Date PreviousDate
from t
outer apply(
  select max(Date)
  from t t2
  where t2.Id = t.Id and t2.date < t.Date
)pd(Date)
left join t pt on pt.Id = t.Id and pt.Date = pd.Date
order by t.Id, t.Date;

Do in 2 stages, first get the previous date then left join

with cte as (
    select
        ID, Rec, Date,
        (select top 1 date from t t1 where t1.id = t.id and t1.date < t.date order by t1.date desc) as Previous_Rec
    from t
)
select cte.*,t.rec,t.date 
from cte
left join t on t.date = cte.previous_rec and t.id = cte.id
order by cte.id, cte.date

https://dbfiddle.uk/IbwFcMn6

I see that you have multiple records for a date and you want to get all previous records for previous date. You can use self join like below to get the desired results:

select s1.*, s2.rec [Prev Rec], s2.[date] [Prev Date]
from   [Source Table] s1 left outer join
       [Source Table] s2 on s1.id = s2.id and 
       s2.[date] = (select max([date]) from [Source Table] 
                    where id = s1.id and [date] < s1.[date])