This paper proposes an architecture of a next-generation Internet eXchange (IX) based on the Generalized Multi-Protocol Label Switching (GMPLS) technologies and the photonic cross-connect (PXC), hereafter referred to a Lambda-IX. At first, we investigate a basic Lambda-IX model where the PXC provides a GMPLS-controlled lambda label-switched path (LSP) to interconnect different ISPs' border routers. We verify that the proposed Lambda-IX model can achieve the lambda-based and resilient interconnection for the ISPs, thanks to the PXC's bit-rate insensitive operation as well as fast restoration operation. In addition, once GMPLS functionalities are introduced on the border routers as well as the PXC, very flexible interconnection can be achieved such as demand-based creation and deletion of lambda LSPs. Next, we initiatively demonstrate an experimental Lambda-IX using a PXC and IP/MPLS routers. A Lambda-LSP with OC-192 bandwidth can be successfully created by using the GMPLS RSVP-TE signaling protocol via a control plane, and an EGP session of Border Gateway Protocol 4 (BGP-4) can be established over the Lambda-LSP created between the GMPLS-enabled border routers via a data plane. We also evaluate the fault recovery operation in the case where such Lambda-IXs are consisted of several PXCs and demonstrate that the Lambda-LSP as well as the corresponding BGP session can be restored with a fast recovery time of less than 1s. Through these investigation and demonstration, it is revealed that the Lambda-IX can be put to practical use aiming at inter-exchanging a large traffic in a near future, while enriching the functions of IX.