Lid dispensers are not universally compatible with all types of disposable cup lids. Compatibility depends on several factors, including the size, shape, and design of both the lids and the dispenser. Lid dispensers are typically designed to accommodate specific lid sizes, such as those for 8 oz, 12 oz, 16 oz, or 20 oz cups. The diameter and style of the lid, such as flat, domed, or sip-through, also affect compatibility. 
Some dispensers are adjustable and can handle a range of lid sizes, but they may still have limitations based on the lid's design. For example, a dispenser designed for flat lids may not work well with domed lids due to differences in height and shape. Additionally, the material of the lid, whether plastic or paper, can influence how well it fits in the dispenser. 
It's important to check the specifications of both the lid and the dispenser to ensure compatibility. Manufacturers often provide guidelines or compatibility charts to help users select the appropriate dispenser for their lids. In commercial settings, using a dispenser that matches the specific lids in use can improve efficiency and reduce waste. 
In summary, while some lid dispensers offer flexibility, they are not universally compatible with all disposable cup lids. Careful consideration of the lid and dispenser specifications is necessary to ensure a proper fit.