mysql query two tables, UNION and where clause

There are two problems with your SQL:

1. (THis is not the question, but should be considered) by using WHERE over the UNION instead of the tables, you create a performance nightmare: MySQL will create a temporary table containing the UNION, then query it over the WHERE. Using a calculation on a field (LOWER(requester_name)) makes this even worse.

2. The reason you get two rows is, that UNION DISTINCT will only suppress real duplicates, so the tuple (someuser,peter) and the tuple (someotheruser, peter) will result in duplication.

Edit

To make (someuser, peter) a duplicate of (peter, someuser) you could use:

SELECT
  IF(requester_name='peter', receiver_name, requester_name) AS otheruser
FROM
  ...
UNION
SELECT
  IF(requester_name='peter', receiver_name, requester_name) AS otheruser
FROM
  ...

So you only select someuser which you already know : peter

You need the where clause on both selects:

select requester_name, receiver_name
from poem_authors_follow_requests
where LOWER(requester_name) = LOWER('user1') or LOWER(receiver_name) = LOWER('user1')
union
select requester_name, receiver_name
from poem_authors_friend_requests
where LOWER(requester_name) = LOWER('user1') or LOWER(receiver_name) = LOWER('user1')

The two queries are independent of each other, so you shouldn't try to connect them other than by union.