The Echo Dot uses a power supply rated at 9W per hour. Using rounded numbers, that translates into a maximum power source of about 5 volts at 1.8 amps per hour. That equals 9 Wh of energy. The Dot will rarely use that much, but the power supply is capable of delivering that amount.

The question of course is how you use the Dot. If the Dot just sits around most of the time waiting for a command, then power consumption will be very low. If you ask Dot a lot of questions or give her a lot of commands, then power consumption will be more. If you listen to music wherein Dot is running constantly, then power consumption will be high. No way to tell how much Dot is consuming at any given time without using a meter, but the most she can ever get from her supplied power source is 9W, or as we saw above 5v at 1.8amps. So we know Dot will never consume more than 9 Wh of energy per hour.

So what is the power rating on your lipstick power charger? I found one on Amazon rated at 3350 mAh. To deliver the energy of 9W for one hour requires 1800 mAh. So for this example divide the 3350 mAh rating of the lipstick charger by 1800.

3350 mAh / 1800 mAh = 1.86 hours at maximum power level

There are caveats though. For example, the lipstick power charger I found one Amazon only delivers 1amp maximum, rather than 1.8, but it will probably work with the Dot.

So to estimate the minimum time your lipstick power charger will power your Dot, divide its power rating (in mAh) by 1800 mAh and you will get the approximate number of hours it will power the Dot. Fortunately, you will likely get more than that depending on how you use your Dot.

ETA: Again, this is a rough estimate of the minimum time a power source will power the Dot. The 9 Wh of energy is the maximum energy that the Dot's power supply can deliver. I doubt the Dot will ever approach that level of power consumption, even when rocking the house with music.