When John Hicks wrote down his IS-LM model in 1937, he meant it as a halfway house between Keynes and what Keynes called "classical economics." And, indeed, it is. You can think of it in any of three ways:
That the LM curve (plus the inflation rate and the risk premium) tells you more-or-less what the real interest rate is, and then the Keynesian income-expenditure function does the real work of determining output, employment, and the shape of the business cycle.
That the IS curve (in its flow-of-funds through financial markets form) tells you more-or-less what the nominal interest rate is and thus what the velocity of money is, and then the quantity theory does the real work of determining output, employment, and the shape of the business cycle.
That the two sets of factors are symmetric, and that whether it is more like a Keynesian or more like a classical theory depends where on the LM curve you are--and on what the local slope of the LM curve is.
Hicks clearly thought of it as (3), Alex Tabarrok and Tyler Cowen think of it as (2), and it seems as though everybody else thinks of it as (1).