Antonyms for the phrase "put the lid on" could include actions such as "opening up," "revealing," or "loosening." When someone puts the lid on something, they are essentially closing it off or shutting it down. By contrast, opening something up would imply greater transparency or a newfound level of accessibility. Revealing a secret or hidden truth could be seen as the opposite of placing a lid on something, as would undoing the progress that may have been achieved by lifting the lid. By loosening or removing the lid, it's possible to gain greater freedom or flexibility, indicating a desire to move away from the restrictions that may have previously been in place.