As mentioned in the article , the LOOKUP() works in a manner where you match one value having common pointer column that has many values for that pointer in the look up table to get a different parameter as return from the lookup table.
LOOKUP("Bob's Burgers", "Restaurants", "Name", "Phone")
So in the expression above “Bob’s Burgers” and “Name” are common pointer parameters. The expression looks for restaurant name “Bob’s Burgers” in the list of restaurant names column called “Name” in the table Restaurants and returns back the “Phone” for that record from the [Phone] column in lookup table “Restaurants”.
In your expression common pointers as well as return value all seem to be dates.
Could you please mention where the highlighted two date values are in Table A or Table B
which table [Date] is there and which table "Date"is there in the below expression?
LOOKUP([Date], “Contact_txn”, “date_from_contact”, “Date”)
and what result you are getting for this expression in expression assistant?
Edit: Or you may wish to share a screenshot of some sample records with dummy data from your both the tables to get an idea of table structure.