The following information is a personal summary. It does not represent a common consensus or discussion of several lipo users. Use at your own risk.
 
On Youtube one can find many videos with boiling, smooking, burning (with flame) or exploding lipo batteries. Most videos are based on intentional violations of the specifications of the batteries. Can that happen with a lipo battery connected to the Pcduino v3, too? The battery interface is a new addition to the Pcduino and you (and the community) might also be new to their handling. Could a non-intentional violation of the battery specifications happen?
 
It turned out, that the current design of the Pcduino does. The AXP209 chip disrupts the power at a voltage of 2.9 v by default. That already violates the battery specification of a minimum of 2.96 v, though slightly. Even worse, after chip shutdown the board continues to draw power and the voltage continues to fall below 2.9 v. As soon as AC power is restored, the battery starts to charge. The AXP209 chip classifies the over-discharged battery as potentially damaged. (Indicated by a reduced charging current until 3 v are reached.)
 
A lipo battery on the Pcduino might not produce the same dramatic effect as in the mentioned Youtube videos, but it might loose it's capacity quickly due to over-discharging. A practical test is still outstanding, though. It's unclear to me whether this issue could be fixed in future revisions of the board.
 
To cut a long story short, if you thought about using a lipo battery as a USV to your Pcduino, forget it if you can't guarantee manual disconnection of the battery. Or quick AC restoration. That's not really the idea behind a USV.
 
Many other use cases, like attended use of robot vehicles should still be fine. (Regarding vehicles, read about physical damage below.)
 
The companion of over-discharging is over-charging. Lipo batteries are designed to be used. Like in RC helicopters. Fly, charge, fly, until next weekend. Lipo batteries are not designed to sit there fully charged or fully discharged for months or years. After prolonged time at the extreme charge states, capacity is permanently lost.
 
It makes sense to me to lower the charge target voltage from 4.2 v to 4.1 v. You sacrifice 10% of the capacity, but you double the lifetime of the battery. Whether that's a good deal depends on your usage scenario.
 
I operate my battery with an increased discharge target voltage of 3.3 v (instead of the default of 2.9 v). This sacrifies around 5% of the capacity, but again extends the lifetime. However, even this setting doesn't solve the issue of the board draining power (3.7 mA) below the target as described above.
 
All in all, I sacrifice 15% of the capacity for a security margin.
 
Temperature is also an issue for the life expectancy of a lipo battery. In a closed casing the Pcduino might heat up the battery to 40°C. With a default charging target voltage of 4.2 v, about one third of the batteries capacity is lost simply due to storage. This is not an issue of the board, but one of ventilation. However, while the board is rated up to 80°C, a connected lipo battery isn't.
 
Safety considerations wouldn't be complete without mentioning physical damage. Most Youtube videos rely on physical damage for their effects. Damage is equivalent to short-circuit.
 
Short-circuits are a problem for lipo batteries. The board features a difficult-to-get JST-SH connector. You won't find a battery with a ready-made five-pin JST-SH connector. Better make sure your home-brew cable is perfectly proof of short-circuits.
 
The battery also has current specifications (above discussion was about voltages). My Pcduino v3( B) draws between 200 mA (idle, voltage 4.1 v) and 700 mA (full load, voltage 3.3 v) from the battery. Charging current is 408 mA maximum. I have no experience how hot a small (200 mAh) lipo battery gets when discharged at 700 mA with an immediate charge at 408 mA.
 
Overview of considerations for handling lipo batteries:
 
*  over-charge above 4.2 v
*  long-term storage at 4.2 v (fully charged)
*  over-discharge below 2.96 v
*  long-term storage at 2.96 v (will drop below)
*  over-current to/from the battery (see the "C" rating)
*  temperatures above 30°C or 40°C
*  physical damage to the cell
*  short circuits (cable, connector, board)
 
One might argue that every household has several lipo batteries in various electronic devices. Without them producing the same dramatic effect as in the mentioned Youtube videos. This is an important argument, because it shows that it is responsible to use lipo batteries.
 
However, slightly inflated lipo batteries are also common. Due to over- or under-use they are in a state where it's no longer safe to charge them. Chargers refuse them. The AXP209 chip on the Pcduino board probably refuses such cells. It's a high-tech product with impressive specifications. However, it seems that the lipo battery interface on the Pcduino is rarely used.
 
The RC community has a lot of experience with lipo batteries. They operate them closer to the limits and their recommendations sound extreme. Like only charging the batteries on a fire-proof surface. I'm not convinced that is necassary if one can assure conservative cell limits. (Easier to achieve with the single-cell battery than with multi-cell batteries.)
 
On a side note, the chip doesn't shut down the system. It disrupts the power. A script executing the shutdown is available here:
http://wt.tuxomania....ownload/axp209/
 
Installation is done by unpacking the archive to / or /usr/local.
Check the contents first. It should unpack files into the
directory /etc/axp209 and one file to /sbin/axp209.sh.
 
You can activate it in /etc/rc.local with the following command:
/sbin/axp209.sh --apply_profile usv_like