The upwards-sloping LM curve gives the interest rate that needs to go with a given income level to accomplish equilibrium in the money market. We again add a third dimension to the i/Y diagram, measuring the price level along this third axis. The question is how the market-equilibrating interest rate changes if we keep income constant and move along this third axis. Two points need to be noted:

The demand for money, which is a demand for buying power, for real money, does not change if the price level rises. With income unchanged, individuals want to buy as many goods per period as before.

As long as the central bank keeps the nominal supply of money fixed, the real supply of money falls as the price level rises during our move out along the third axis.

So if the interest rate remained unchanged, as we move out the price axis, an excess demand for money would arise and grow bigger and bigger. To prevent this, the interest rate needs to increase. This makes holding money more expensive and induces people to hold less money. The money market can be in equilibrium at a lower money supply.

The crux of this is that the LM plane slopes up as we move along the price axis.