I have two tables (t1, t2) to join based on id and year-month YYYY-MM

Generally, the join goes like this for example:

SELECT t1.id, t1.month, t2.price
FROM t1
JOIN t2
ON t1.id = t2.id AND t1.year_month = t2.year_month

Now, for one specific t1.id, say t1.id = 'a', I need to join with the previous month on t2
I.E.

SELECT t1.id, t1.month, t2.price
FROM t1
JOIN t2
ON t1.id = t2.id 
AND (t1.year_month = t2.year_month if t1.id != 'a' 
     else t1.year_month = t2.year_month - 1 month)

What I think to do is to create a temp table that year-month on t2 for id = 'a' is increased by one month. But t2 is a really large table so I don’t really want to go with this route.

What is the best way to achieve this? Thanks!