What you are probably really wanting to do here is use the union operator like this:
(select ID from Logo where AccountID = 1 and Rendered = 'True')
union
(select ID from Design where AccountID = 1 and Rendered = 'True')
order by ID limit 0, 51
Here's the docs for it https://dev.mysql.com/doc/refman/5.0/en/union.html