Solution:"Lender of last resort" is the word used in context of RBI giving loans to banks. So, #2 is right.For #3 (Giving loans to the government) = Appropriate word is "banker to the government".
Now some candidates may argue that #3 is also suitable for the word "Lender of Last resort" but we have to go by the rot-learning/explanation given by academic books on banking systems such as Prof Bharati Pathak and E.Narayan Nadar.
In previous exam also UPSC asked a similar question about the "What is the meaning of RBI is "bankers Bank"?" And there too, UPSC examination had gone by the interpretation of academic books.
#1 (Loans to industries) not directly done by RBI. At best RBI will open some special Windows to give loans to banks and NBFCs who will then indirectly give loans to industries e.g. LTRO, SLTRO etc. So, #1 is wrong.