M1 reserves are not lent out by commercial banks - they are a liability of the central bank and an asset of the commercial banks or anyone else with access to the central bank's balance sheet. Banks only ever lend you their own liabilities. E.g. if you get a loan from HSBC, you borrow HSBC pounds because you have a deposit with HSBC.
When banks lend, they create a deposit (or credit an existing one) in the name of the customer (liability), and create a corresponding loan (asset) on their balance sheet. Banks don't _need_ reserves, like warehoused cash, to lend. They just need a capital buffer to absorb any credit losses on their loan portfolios.
The M2 money supply only increases if banks lend. In theory, they are more ready to lend when they have a better capital and liquidity position, which an injection of reserves is intended to achieve. But if no-one wants loans then M2 money supply doesn't increase as a result of a higher M1 money supply.
Also, "fractional reserve banking" is not a concept that relates to modern banking. Banks can lend as much as they like within reason. They are no different to any other business which can leverage their balance sheet by adding debt to increase return on equity. Loan creation is limited by:
1) Capital requirements - whereby loan creation is a function of how much capital they have, how risky their existing assets/loans are and how risky incremental loans are
2) Demand for loans from customers, which is a function of the macro environment e.g. interest rates