Since your battery will be running at 3.7v max(-ish), it's safe to monitor it's voltage without a voltage divider. I'd double check this with someone else, because I've never done this myself, but I am pretty sure all you really need to do is plug in a wire coming from the battery's + lead into an arduino's analog pin (the only reason I question this is because I don't want you frying your board because I missed something). Then, using the analogRead() function, you can monitor the analog version of the ratio between your battery's voltage and 5v. You'll need some baselines, so you'll want to use a multimeter to measure the actual voltage of the battery and record the value your Arduino reads (or you can just do the math and equate the ratios - x/1023 = Vin/5v - where x is the output of the analogRead() function).
Once you get all that, all you need to do is "graph" it on your choice of lcd. The simplest option is an LCD w/ a HD44780 chip (very common lcd driver). You can read how to run it here:
If you want to simply write the percent-battery left, you'll want to find what the battery's (or the boost regulator's - which ever comes first) cutoff voltage is, and do some more math to figure out how much percent battery life is left depending on what you get for Vin - (should be something along the lines of (Vin - Cutoff) / (Vmax - Cutoff) = x / 100
where x is your percent value, vmax is the maximum battery voltage (should be around 3.7V), vin is the actual voltage, and cutoff is the cutoff voltage for either battery or boost reg.
hope this helps and hope I didn't make a mistake somewhere 