Issue with a lookup formula

Here is the issue I’m having.

I have two tables. Table A (4 Columns) and Table B (4 Columns)

In table A, I have Column_1 which is formatted as a Lookup Column for Table B.

In Table A (Column_2), I wrote formula to look up Table B and display the value in Table_B (Column_2) that is associated with the matched value in table A (Column_1).

However, because Table_A (Column_1) and Table_B (Column_1) are formatted differently (i.e. Text Column vs. Lookup Column) the formula that I wrote does not work. However, Table_A (Column_1) needs to be formatted as a Lookup column–and it is also not possible for Table_B (Column 1) to be formatted as a lookup column.

As such, my question is, how put together a basic index-match equivalent formula that factors in the difference in formatting between the Lookup column, Table_B (Column_1) and Match column, Table_A (Column_1)?

Thanks