"Data Lakehouse" is sadly term ruined by AWS. It used to mean "data lake extended to support data warehouse use cases". So something like HDFS or S3 with Delta (from DBX) or Apache Iceberg storage formats, utilizing Spark or Presto/Trino or something for compute. One unified platform built on scalable big data technologies, that can do transactions, SQL MERGE, smart partitioning and other bells and whistles. Then AWS…
I've understood and implemented differently. With Spectrum (or Polybase for SQL Server / Synapse), you can extended into the data lake. Copy over aggregate/curated data or something you need to special use cases on. Leave the structured, columnar data within the cheap storage. You pay per scan but it is cheap (at least to a point).
Also, Databricks took the Lakehouse moniker and sprinted with it. AWS was late to the game from what I saw (at least for marketing terminology adoption).