How do I cause one switch to "lock out" other switches in parallel?
This scheme uses the difference in relay pick and hold voltages to do what you require. It has the small disadvantage that 2-pole foot switches are required.

DC relays typically pick at about 2/3 of their rated coil voltage and will remain on until the coil voltage drops below 1/3 supply. (These figures are very rough.)







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Figure 1. Relay interlocking.

How it works:


If SW1 is pressed the coil of RLY1 will be energised and the contacts will close. When the footswitch is released the coil will remain energised via R1, D1 and the hold-on contact.
If SW2 is pressed RLY2 will pull in. At the same time the common hold-on supply will be shorted to ground and RLY1 will drop out. 
The spare contact of each relay can be used to control your "LED".
R1 limits the current during short circuit.
The diodes prevent back-feed onto the hold-on rail.


R1's value will need to be established by experiment. A value close to the coil resistance should give you 1/2 supply on the coil and this should be sufficient.

R1's power rating should be high enough to cope with a switch being held on indefinitely. e.g., On a 12 V supply, \$ P = \frac {V^2}{R} = \frac {12^2}{470} = 0.3 \; W \$.







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Figure 2. By using changeover contacts only the highest priority switch will feed the "LED" load in the event that multiple switches are pressed.

If you just want switch priority then Figure 3 would suffice.







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Figure 3. Simple switch priority.