Please carefully check out your source, there is no EL/M-2052 anywhere.
Rough idea of radar placement on LCA
Highlighted portion is the almost space available for Radar. Rest is occupied with other equipments.
View attachment 21823
Also checkout the radome design which shows size limitations for Radar.
As per the official website of Thales RBE AESA designed for LCA is smaller and lighter than RBE2-AA , it means Thales found their available Radar not suitable as per RFQ released by HAL.Hence they modified it as per the specifications mentioned in RFQ.
Link for RFQ:
http://hal-india.com/Common/Uploads/TenderDoc/10364_TenderPDF1_RFQ_AESA.zip
Unable to find the links for Annexures mentioned in RFQ.
Hence, I can say, Rafale's RBE2-AA (in original form) as in quoted image can be a suitable contender for LCA.
Extra stuff:
EL/M-2052 showing the two module architecture of the new system, designed to fit into compact spaces like the LCA nose cone
ELM-2032 with LCA's cone on a testbed