Does slowly charging a battery extend the lifetime? -Why?
Short answer: Yes.

Before giving the long answer, think about how fast-charging a lead-acid battery works.  Applying a lot of current raises its voltage; however, the negative plates are not able to react with the sulfuric acid quickly enough, and so the excess voltage is not helping it charge faster.  On the other hand, the high voltage does damage the inside of the battery, thus reducing its life.

Long answer: when lithium ion batteries are given the high amperage, they are unable to "refuse" fast-charging, like lead-acid batteries do.  As a result, the chemical reactions are forced to happen at a quick rate.  Some chunks react quicker than others.  The end result is, uneven charging of the battery.  This unevenness adds up with time, and its capacity decreases.

Now the point is, any speed of charging for a lithium ion battery causes unevenness.  A faster rate causes more unevenness; a lower rate causes less unevenness.  If a battery heats up while getting charged, it is more malleable, and accordingly more susceptible to damage.  Therefore, no matter how slowly you charge a lithium ion battery, over time its internal organization decreases, and it loses capacity.

Note: I am sweeping a lot under the rug to give a simple answer.  The underlying reactions that I am calling unevenness have to do with how well the lithium ions can travel between the positive and the negative electrodes, and also whether they get converted to a different form due to local overcharging/overdischarging.  I can give more detail if you're interested.  The exact chemicals depend on the type of lithium battery.