I can speak with the experience from RC hobby battery use. In most instances, Lipo batteries are charged with a current rate that matches their capacity. For example, a 2.2ah battery would be charged at a rate of 2.2 amps. This would charge a theoretically empty battery in roughly 1 hour. Most devices which use Lipo batteries don't allow the battery to be fully discharged, Lipo batteries are damaged quickly by over discharging or over charging, even a little bit. There are certain voltages the cells must never go below or over. The Battery Management Circuit in the device is responsible for maintaining this.
With a lot of RC hobby batteries, the charge rate can be quite high, as high as 10C, meaning 10 times the capacity (C). So a 3ah battery could be safely charged at a 30 ah rate. This should only be done if the manufacturer states the battery is designed for this rate. Of course, the slower the charge rate, the longer the battery will provide good service.
Usually somewhere on the battery label the manufacturer will list the "C" value for the battery. If a value of 2C is listed, then charging a 2ah battery at a 4ah rate is safe. If this rating is not provided, it is best to charge at a rate equal to the battery's capacity or lower.
I have been flying RC helicopters for years, these use large Lipo batteries. I have always charged at no more than a 1C rate. I like to get as much life out of my batteries as I can, they are quite expensive.
Hope this helps.