I would not try to force it by opening the lid. Get underneath and push on the lift part and try to determine why it's not moving. There are a lot of different mechanisms and many are not attached to the wood all that securely, so if you try to force it you'll most likely pull the anchors out of the wood, and not budge what is sticking.
I have one that has a metal rod that is like a big screw, and the lift rides on that so it can easily get a bit rusty and not want to move. I have others with cables and if the pulley gets jammed, it won't go. And others with a chain and those seem to bind up along the wood. I've seen plenty were something came loose and you can not get it to open without external help (like a hand underneath).
With all that can get hung up, I understand why Singer went with the manual lift for the machines - the operator is the one doing the lifting.