It's not a GUI, but saw[0] was my go to for grepping, streaming, and searching CloudWatch logs.
Cool. I had a similar use case and created a tool to stream colorized logs from CloudWatch to your terminal that is a little more ergonomic to use than this:
Saw: https://github.com/TylerBrock/saw -- Stream (tail -f) colorized AWS CloudWatch logs
Yeah, don't use the web UI. An alternative to awslogs is saw, https://github.com/TylerBrock/saw. Me likey..
Regarding the tooling: I hated debugging Lambdas via CloudWatch logs when using them for Hustle, it drove me to drink.
I eventually got upset enough that I made a tool to stream the cloudwatch logs to the terminal and colorize, indent + nicely format json output: