The plants need fresh air. How is your lung room ventilated? Does it get fresh air? Is it it's own HVAC zone? If it's somewhat closed then you are filtering used air and putting it back into your tent. Forget the Co2, that's another unnecessary expense.
There's nothing 'wrong' per say about your setup. If that's what you want to do, it's your grow. However, you've incurred some needless expense for little to no benefit for your plants. Indoors, inside a tent the purpose of the filter is to limit the smells. That's it. It's not to provide 'clean' air. You want the air inside the tent to have an exchange with fresh air outside the tent, the exhaust fan does that. You can have an exchange of air w/o the filter.