Integrating gRPC with AWS Lambda presents challenges due to the incompatibility between HTTP/2, which gRPC requires, and AWS API Gateway's reliance on HTTP/1.1 for Lambda calls. While gRPC services cannot directly run on AWS Lambda, workarounds such as using a web proxy on Lambda to forward REST requests to a gRPC service or deploying gRPC-Web allow limited functionality. gRPC-Web operates over HTTP/1.1 and can be accessed from JavaScript clients, although it has limited client support. The article also suggests using Earthly for simplifying build automation in serverless architectures and calls for more gRPC-Web clients to make Lambda-based gRPC services feasible.