wordpress ajax relationship query

Look at the very last part of that query– LIKE '%\"17497\"%'. You are searching for any characters, followed by literally "17497", followed by any characters. I am pretty sure that is not what you want. I think you want any characters, followed by 17497 without the quotes, followed by any characters.

That means the meta_query is written incorrectly.

$meta_query = array(
    'key'       => 'lineup_artists',
    'value'     => $ArtistID,
    'compare'   => 'LIKE'
);

You don’t want to be adding your own quotes like that.

You also want to be checking that $ArtistID has a value before trying to use it, and you should be doing some data sanitization and validation before using information in $_POST. $_POST data is not safe data.