I have used these things in the past, normally signal reference is tied to ground if you have a split supply. Now the maximum supplies you would run at are a split 30V, so you cant get more than that at the output pin . Your measurement has to be faulty, possible related to the way you are grounding things. If the reference voltage is not at ground(you have a single sided supply), then you need to use an amplifier to get it back to a ground reference suitable for the ADC, since chances are that the ADC will have a ground reference at some point.
As far as the voltage is concerned, a simple voltage divider would do it, but you need to take into account the input impedance of the ADC if it is low, as well as the input capacitance, the series R can't be too large either if it limits your bandwidth. If that won't work, then a voltage divider followed by a buffer amplifier will. You have to check the input characteristics of your ADC from the data sheets.
The sampling rate is also something to consider. Although the signal band width is probably limited by the mechanical response time of the LVDT, the bandwidth of the system and the ripple at the output need to be taken into account, sampling theorem stuff,
cheers,
Richard