Ok, if you are desperate you can use your power supply to charge a LiPo battery, but I prefer my iMAX lipo balance charger. Costs less than 20 bucks at eBay and has all the features you need, like automatic stop charging after some time or even after some energy, and works perfectly for my 3s and 4s copter batteries as well (these bigger batteries have a big main connector, usually EC3 or XT60, and a smaller XH connector which is connected to each cell for balancing).
BTW, what do you think about parallel charging LiPo batteries? I have
this extension for my charger and I've used this with up to 4 batteries in parallel. Of course, before start charging I measure all batteries, and I don't connect two batteries in parallel, if the difference is more than a few 10 mV for one cell, to avoid high balancing currents (once I connected the balancing connector backwards and then the main connector and after this I had to solder a new connector to the battery, because the sparks caused some bad black deposits on the contacts). But I've read you should do this with batteries with the same capacity (and age) only, but why this limitation? Once the voltage is the same for all cells of all batteries, it shouldn't matter.