How to choose Li-ion or other battery for uC (packed into thin small device) and connect
(1) Power options that are ideal specifically for a thin/small device:


If you want a simple way to scale the device size down, I suggest a primary Lithium coin-cell; available in various small sizes and easy to integrate (no protection circuitry necessary, etc.). Example: Energizer CR1632 130mAh cell
If you want rechargeability, you might want to try Lithium-ion/secondary cells. They are available in a variety of capacities; Example: 110 mAh Polymer Lithium-ion battery
Alternatively, you can combine some of the advantages of both systems and go for a Li-ion rechargeable coin cell. Example: 40 mAh LR2032 cells


(2) If you go with Coin-cells:
These cells allow "small" current draws, I believe limited to around 20 mA continuous draw (i.e., except short bursts). However, if the LCD is a low-power-consuming one (think of a segment LCD found on digital calipers), then you should be able to get by with a coin-cell or even a button cell.

(3) If you go with Lithium ion:
If this is a personal project, perhaps you can unplug the battery yourself when it's low, and charge it externally using a separate board/circuit. But if you want integrate charging on-board, you might consider a charging IC such as MCP73831T.
Also, if you go the Li-ion route, make sure to ensure that the battery you buy has protection circuitry integrated into the battery (many Li-ions do so, for example the Sparkfun one I linked to above.)

(4) About powering the microcontroller:
Obviously, to find out the spec you requested ("power usage of uc"), you need to consult the datasheet of the microcontroller that you want to use!
You also need to consider what voltage at which you want to run the microcontroller and circuit. For example, if you choose to run the circuit at 3.3V (e.g., for compatibility with your optical sensor), then you need to either use a boost/stepup regulator (for the  coin cell case, where the voltage is 3V) or use a LDO regulator (for the Li-ion case, where the voltage which lies between 3.4V and 4.1V, for a majority of the cell's discharge cycle).

(5) Lastly, regarding low-power optimization:


You can obviously put as many parts on the circuit as possible to sleep/shutdown mode between measurements (or whatever it is you are doing) to minimize current draw at non-active times.
For the LCD, you can try a small, simple segmented numerical LCD to really optimize the power consumption, but based on what it is you are displaying, you can also step it up to a graphic LCD or OLED, possibly even TFT (if you cut down on the backlight), and still stay under a few milliamps: Read this interesting comparison of power consumption of some display options.