Generally speaking the maximum charge current with LiPo batteries is 1C. Most of the datasheets I've read recommend 0.5C but many allow up to 1C before stating that the battery's life will be shortened.
Here's a picture I grabbed from the web showing the two stages of LiPo charging for a single cell (3.6V battery). There's a constant current phase until the battery voltage reaches exactly 4.2V. This will happen at about 80% of capacity. Then the charge voltage is held at 4.2V while the current slowly drops off. The current will never hit zero so the charger decides what a 100% charge is. If the charger isn't too smart, it'll keep charging forever - that's when your laptop says "Charging: 99%" for hours and hours!
So if you have a battery pack that is rated at 2200mAh you may charge at up to 2200mA (ie: 2.2 amps) for approximately 1 hour (it will take longer due to the way the charger works) but preferably at half that - 1.1 amps for roughly 2 hours. In addition, if the battery pack is (say) 14.8V, the charger must be designed to charge for that voltage. LiPo require very accurate charge voltages and severe damage will result if you not comply.
I'm sure there's a lower level current below which the battery will not charge or take an infinite amount of time to charge. It's probably very small though. There's a 500mA charger on my desk which I've used to charge some 10,000mAh batteries. That would be a rate of C/20. So it takes ages but it does work.