Putting the IS and LM Curves on the same diagram (by assuming that the interest rate is the same for both) alows us to find an equilibrium level of income and the interest rate.
The LM Curve traces out those point consistent with equilibrium in the supply and demand for money.
We can use the Simple Keynesian Model to derive an IS curve simply by letting investment be a function of the interest rate.
We can also put the interest rate on the vertical axis to emphasize the role of that variable. This produces a clear (to many people) view of the derivation.