That doesn't exist per definition. You cannot have a light client that its own node and it is not the node defined in the specific blockchain. The bitcoin innovation was about using a common ledger for every node and the nodes must run specific code to check that the blockchain state is the correct one.

If you find a way a node can do less work that what is doing now without relying on another node you would discover something new at the computer science level, so this light node will transform into the definition of a node.