In the following I'm using an MSP430F20.. as an example. Results should be identical or similar for most MSP430s, BUT check the data sheet for the part you are using!!! YMMV.
Most (not all) MSP430's have a 1.8 - 3.6 Volt operating Vdd range.
Vdd is the absolute maximum operating voltage. Absolute maximum non operating voltage is typically 4.1 V.
If you want full rated clock operation you'll need a voltage near to 3.6V. As an example only, figure 1 page 20 in http://focus.ti.com/lit/ds/symlink/msp430f2011.pdf shows that you require Vdd >= 3.3 V and <= 3.6 V for full speed operation.
Below 3.3V, max allowed clock speed drops linearly with supply voltage down to 2.2V min for programming or 1.8V min for operation.
If a LiFePO4 cell is moderately heavily loaded it will deliver most of its capacity above 3.0V. A MSP430 processor can be run at about 70% of rated maximum clock speed at this voltage.
Maximum voltage: A LiFePO4 has a maximum safe fully charged voltage of 3.6 Volt. It is possible but immensely unwise to charge them above this. Notionally a LiFePO4 may thus have a terminal voltage in excess of the MSP430 max operating voltage but this is extremely unlikely to occur or to matter in practice. If you wanted to be completely certain a shunt regulator could be used to bleed the small "tail" of voltage above 3.6V after the battery had been fully charged.
Minimum voltage: As above, the processor needs >= 3.3V for full speed operation. A lightly loaded liFePO4 (say loaded at no more than 10 hour discharge rate = C/10) will deliver almost all its energy at >= 3.3V. As loading increases terminal voltage falls for a given % of discharge. eg at C (1 hour rate) it would typically drop below 3.3V with around 80% of its capacity remaining.
A LiFePO4 will still be well above 1.8V or 2.2V when safely fully discharged.
if a LiFePO4 cell is used to directly power an MSP430, maximum voltage will be safe for most purposes and protection could be provided against battery overcharging.
If the battery is lightly loaded (C/10 or less) then the processor can be run at full speed for the whole of the battery life.
If the processor shares the battery with a device that loads it heavily (eg a motor or heater or ...) then reduced maximum processor speed will be required.
If both full speed operation and greater than C/10 battery discharge rate is required then a boost converter is required to maintain Vdd voltage.
If the controller is crystal controlled and if a supply independent ADC reference is available then operation directly from a LiFePO4 cell seems entirely acceptable.