Try Searching for "router lift"
Jesse-em makes a decent one, and there are other manufacturers that do too. My Powermatic cabinet saw came with their option from the factory. The mechanism is stout, but the size of the plate that holds the device in your table is where things can get sloppy. Routers (esp for table based functions) are heavy. Sag in the integrated table plate needs to be kept to a minimum to maintain accuracy. The table that supports the plate is usually rabbeted to mount the plate flush. This table (and the rabbet) need to be able to support the whole assembly and remain sag-free to maintain accuracy as well.
I would not trust a melamine outfeed to support this and be sag free. There are manufacturers that make steel tablesaw wings fit for these lifts, and I would suggest one of those.
In "theory" only the plate that holds the lift needs to be flat since that is where the work is being done, and the whole plate can be shimmed to be proud of the sag in the table to keep infeed/outfeed support for long work, but this is problematic when the table is on the tablesaw as the rip fence needs to be able to pass over the plate when the saw is needed for ripping. It also means that any router setup that requires a fence (99% of the time) must be broken down to rip work over a certain width. Just my two cents.