There are a few things being confused here.
First it is important to separate what stores information in the data warehouse from what reads information from the data warehouse to produce reports.
For storing information in the data warehouse, you have the choice of using an ETL or a DCC.   If you have not customized what information is being stored, you should always use a DCC (much faster).    If you have customized the information being stored, currently you need to use an ETL, but keep an eye out for DCC enhancements that allow you to customize what data is being stored (and what data sources are being used).
For reading information from the data warehouse, you have the choice of Cognos (aka Insight) Report Studio or the Jazz Report Builder (or just use SQL).   I'd recommend always trying the Jazz Report Builder first, and only if that doesn't allow you to create the report you want, fall back on SQL or Cognos.

The above was all bout the Data Warehouse.   As an alternative to the Data Warehouse, there is LQE.  
Unlike the Data Warehouse, you do not store information in the LQE by either an ETL or DCC, but rather by a TRS (tracked resource set).  
For reading information from the LQE, you have the choice of the Jazz Report Builder (not Cognos) or SPARQL (not SQL).   As with the Data Warehouse, I'd recomment always trying to use the Jazz Report Builder first, and only if that doesn't allow you to create the report you want, fall back on SPARQL.

Now to your actual question:
It doesn't make sense to talk about configuring JRS to use LQE instead of DCC (LQE is a data source ... DCC is a data collection mechanism).   So you can have JRS use LQE instead of the Data Warehouse (different data source choices), or you can have JRS use ETL instead of DCC (different data collection mechanisms).   Which did you have in mind?

WRT your comment, note that there is no such thing as an "ETL Report" ... ETL is a way of storing information in the Data Warehouse, not a way of producing reports.   The only reason to use an ETL instead of DCC is if you have customized what data is being stored in the data warehouse (in which case, today, you have to use an ETL and not a DCC).   The main thing you cannot do is use both an ETL and a DCC to read data from the same data source and write to the same Data Warehouse.

Why not using DCC collection Jobs? They do exactly the same than the old ETL jobs, but smarter and faster. DCC is writing in same Datawarehouse and everithing is available from Insight like it was with ETL jobs.

LQE can reside parallel to DCC, so you always can have both in parall.

regards
Guido