I cannot see how the quality of grace displayed by David here, in his lament for his enemy Saul, can be interpreted either as human mercy or as divine grace (in the sense of a compassionate spiritual gift granted by God). Praise for a fallen adversary does not involve either of these things. It involves grace as a quality of the mind and character, the quality that makes one gracious. This can be defined, I think, as a combination of the qualities mentioned above: a nobility and generosity of spirit.

"gracious
a : marked by kindness and courtesy <a gracious host>
b : graceful
c : marked by tact and delicacy : urbane
d : characterized by charm, good taste, generosity of spirit, and the tasteful leisure of wealth and good breeding <gracious living> "
http://www.merriam-webster.com/dictionary/gracious

Not all these definitions are relevant here, but I think kindness and generosity of spirit, along with a certain refinement, are what the commentator is referring to by "grace".

It could also involve a projection back onto the OT of the later veneration of David as God's chosen annointed king, who therefore enjoys divine grace: who is in a state of grace (sanctification). Primarily, however, I think it refers to the inherent noble qualities of David that are seen as making him worthy of God's favour.