I'm not particularly versed in lock-in amplifiers. I once learned about it during my university time.
From your description a lock-in amplifier is probably not the right tool. I assume your strain-gauge bridge operates from a DC supply voltage. If so, there is no signal to modulate and thus no signal to demodulate. A lock-in amplifier is useless here.
You could use a lock-in amplifier if you operate the strain-gauge bridge from an AC supply voltage. You can then use the same AC source as the reference signal. The signal from the strain-gauge bridge is then an AC signal modulated by the bridge unbalance. By multiplying this signal with the original AC frequency, the lock-in amplifier cancels all error components in the signal that do not have the same frequency as the AC source.
While this is technically feasible, it will not make sense in terms of effort/use ratio.
In your application it is probably better to stick with an instrumentation amplifier (
http://en.wikipedia.org/wiki/Instrumentation_amplifier) which will cancel any offset voltages (and common mode disturbances) but will amplify the differential signal froim the strain-gauge bridge.
You don't have to vuild one yourself, you can buy them as integrated circuits, too.
Harald