I'm learning about AWS Lambda and I'm worried about synchronized real-time requests. The fact the lambda has a "cold start" it doesn't sounds good for handling GET petitions.
Imagine a user is using the application and do a GET HTTP Request to get a Product or a list of Products, if the lambda is sleeping, then it will take 10 seconds to respond, I don't see this as an acceptable response time. Is it good or bad practice to use AWS Lambda for classic (sync responses) API Rest?
Like most things, I think you should measure before deciding. A lot of AWS customers use Lambda as the back-end for their webapps quite successfully.
There's a lot of discussion out there on Lambda latency, for example:
In December 2019, AWS Lambda introduced Provisioned Concurrency, which improves things. See:
You should measure latency for an environment that's representative of your app and its use.
A few things that are important factors related to request latency:
Update 2019-12: see Predictable start-up times with Provisioned Concurrency.
Update 2021-08: see Increasing performance of Java AWS Lambda functions using tiered compilation.