note: this is not an innocent peasant whom we captured for sport, but a hardened criminal and a murderer (and a goblin to boost). his possible future execution is not in contradiction with a 'good' alignment. there are many ways to play a good-aligned character, and they do not all imply a ghandi-like attitude towards the world.
There is great latitude, and as long as no gratuitous acts of violence or injustice are committed or condoned, i would think the character would still be good.
in addition, racial traits also should be considered, and fro example- the measure of what a dwarf consider decent or good with regard to other dwarves or humans could be very different from what would be acceptable to do to an orc or a goblin.
In fact, it could as easily be argued that an extreme 'lawful good' (e.g. a paladin-like character) might insist that the evil goblin would be immediately punished appropriately for his misdeeds, and that death would be a most fitting punishment.
my recommendation is to devise a 'personality' for your character (which does not have to have anything to do with your own), somewhat based on the basics in the character sheet, and play the role in a consistent way, as to make it fun for you (and everyone else). the game structure is highly flexible and one should not be shackled to a word.
here is a basic description of the alignments, from the Player handbook:
Lawful good (LG) creatures can be counted on to do the right thing as expected by society.
Neutral good (NG) folk do the best they can to help others according to their needs.
Chaotic good (CG) creatures act as their conscience directs, with little regard for what others expect.
Lawful neutral (LN) individuals act in accordance with law, tradition, or personal codes.
Neutral (N) is the alignment of those who prefer to steer clear of moral questions and don’t take sides, doing what seems best at the time.
Chaotic neutral (CN) creatures follow their whims, holding their personal freedom above all else.
Lawful evil (LE) creatures methodically take what they want, within the limits of a code of tradition, loyalty, or order.
Neutral evil (NE) is the alignment of those who do whatever they can get away with, without compassion or qualms.
Chaotic evil (CE) creatures act with arbitrary violence, spurred by their greed, hatred, or bloodlust
a more in-depth analysis. not official, but fairly interesting
http://easydamus.com/alignment.html