Is it possible to read calculator LCD values?
It's possible to do, though painful and tedious. The display is "bare glass" and no doubt a multiplexed type. There are 28 conductors, including probably 4 commons for a total of 88 possible segments total (including decimal points, indicators etc). 

The LCD will use a complex stepped waveform (probably 4 possible levels) on the commons and segment lines to determine whether a given segment is on or off. 

You would have to capture the levels on each line and determine whether the segments were supposed to be on or off, then relay that information. For example, you could trigger off of the edges in one of the commons and then sample all the other lines using an ADC. 

See application notes for "multiplexed LCD" display for more information on the waveforms to expect. You would need an oscilloscope or this would be too challenging, I think. 

Edit: for example: http://ww1.microchip.com/downloads/en/appnotes/01428a.pdf