When the exchange rate is fixed, this fixes the position of the IS curve. The FE curve is tied down by the world interest rate (ignoring depreciation expectations). So these two curves alone determine income. The position of the LM curve depends on the money supply, which is now endogenous, accommodating the needs of the foreign exchange market. Market forces always drive the money supply so as to move the LM curve into the point of intersection between IS and FE.
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This has the advantage that if we analyse policy measures or changes in the economic environment under fixed exchange rates, we only need to trace what happens to the IS curve and the FE curve. The LM curve may be safely ignored, since it cannot lead a life of its own.
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As examples of how the Mundell-Fleming model may be put to use under fixed exchange rates, you may view animated displays of the consequences of
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an increase of government spending
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or of
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an increase of the world interest rate.