As far as I know, the broking and lending services are carried out by different entities. The broking services are carried out through Zerodha Broking Limited and Zerodha Commodities Private Limited whereas lending is done through Zerodha Capital Private Limited.
You can always access the companies’ financial statements from the portal of the Ministry of Corporate Affairs, to verify for yourself the solvency of the said businesses.
Also do check out this thread on Zerodha’s latest offering - Loan against Securities