Does it make sense to get data from REST API and store it as JSON in an Azure Data Lake? Or the data should be stored directly into Azure SQL?
I've tried both options, but it's not clear in which scenario it is worth to save the data into Azure Data Lake.
Yes this is a perfectly normal pattern that has emerged for collecting large volumes in particular. Writing to a database is great but there are (at least) two aspects to consider:
Data Lakes in contract are schema-on-read, ie you do not have to know the schema in order to write to the lake, so you can just land it and figure out the other stuff later.
This does not necessarily apply to your other question about Synapse as you run the risk of losing your perfectly good SQL Server datatypes. Look at one of the migration wizards for that instead.