My intention is to run an LCD on a FIO with an attached Xbee and wondered if you foresee any problems with current created by that combination while using the 850mAh battery that I got for that use.
Current is created by the battery. It is consumed by the FIO (easy to measure), the XBee (known, if you know the ratio of receive and transmit time), and the LCD (measurable, but the data sheet will probably tell you).
The current consumption will tell you how long the battery will last (approximately).
I am not so worried about how long the battery will last between charges as I am about damaging any of the components involved in that arrangement.
You can't damage a component by powering it from a source that can supply more current than it needs. If you could, the dash lights on your car would be in serious trouble, since there is no way that they draw as much current as the headlights. Or the starter.
You can't damage a component by supply less current than it needs. Your starter motor is not damaged by the battery on the car going dead in the winter. It simply fails to produce the desired affect.
I haven't been able to find what the maximum current allowances are on the Fio or LCD.
What do you mean by allowances? The current that the FIO can supply to any given pins is documented. The current that the FIO can supply to all the pins is documented.
I am using the Sparkfun LCD-09054 amber on black 2x16 display.
That "link" doesn't work.