It really is up to you. There's nothing in the rules that'd prevent it - 4e doesn't enforce alignments. That's a departure from earlier editions, where alignments had mechanical meaning. In 4e, they are there purely for flavor and you don't need to worry about breaking something by changing them.
There's nothing in the nature of goblins that makes them evil, and even if there was you could change that as it's your world. Even in some other editions, when they say "Always Evil", that's meaningless. If that line bothers you, make up goodlins. There are, after all, good undead in D&D 3.5.
Not everything is quite as variable, though. Demons are usually beings of pure evil. Saying demons can be good has ramifications. No one cares about the goblins.
So why are goblins evil? Because that's the stereotype, and a game has to fulfill stereotypes before it can deviate from them, or at least that's the approach D&D tends to follow. In the world you describe, most would perhaps be evil because those are their cultural norms, reinforced by social injustices of others. A goblin's strive for goodness against such forces would make for a compelling story.
You ask, can specific references be found as to what constitutes a good or evil act in 5e.
Ideals
Ideals are one area to look. In the PHB (p124) under ideals, it says:
Your ideals are the things that you believe in most strongly, the fundamental moral and thical principles that compel you to act as you do. Ideals encompass everything from your life goals to your core belief system.
That section goes on to list ideals for the various backgrounds. Many of the ideals are tagged with good, evil, lawful, or chaotic. I've listed the good and evil ones below.
Based on the descriptions, good is associated with beauty, charity, generosity, the greater good, and respect. Evil is associated with greed, mastery, might, power, and retribution. Although the items are generally more attitudes than specific acts, you can make some extrapolations based on the ideals.
Good ideals:
- Charity. I always try to help those in need, no matter what the personal cost. (Good)
- Charity. I distribute the money I acquire to the people who really need it. (Good)
- Charity. I steal from the wealthy so that I can help people in need. (Good)
- Beauty. When I perform, I make the world better than it was. (Good)
- Respect. People deserve to be treated with dignity and respect. (Good)
- Generosity. My talents were given to me so that I could use them to benefit the world. (Good)
- Greater Good. My gifts are meant to be shared with all, not used for my own benefit. (Good)
- Respect. Respect is due to me because of my position, but all people regardless of station deserve to be treated with dignity. (Good)
- Greater Good. It is each person’s responsibility to make the most happiness for the whole tribe. (Good)
- Beauty. What is beautiful points us beyond itself toward what is true. (Good)
- Respect. The thing that keeps a ship together is mutual respect between captain and crew. (Good)
- Greater Good. Our lot is to lay down our lives in defense of others. (Good)
- Respect. All people, rich or poor, deserve respect. (Good)
Evil ideals:
- Greed. I will do whatever it takes to become wealthy. (Evil)
- Greed. I’m only in it for the money and fame. (Evil)
- Might. If I become strong, I can take what I want—what I deserve. (Evil)
- Greed. I’m only in it for the money. (Evil)
- Power. Solitude and contemplation are paths toward mystical or magical power. (Evil)
- Power. If I can attain more power, no one will tell me what to do. (Evil)
- Might. The strongest are meant to rule. (Evil)
- Power. Knowledge is the path to power and domination. (Evil)
- Mastery. I’m a predator, and the other ships on the sea are my prey. (Evil)
- Might. In life as in war, the stronger force wins. (Evil)
- Retribution. The rich need to be shown what life and death are like in the gutters. (Evil)
Dragons
The descriptions in the Monster Manual describe the chromatic dragons as evil and the metallic dragons as good.
The chromatic dragons are described as aggressive, gluttonous, vain, powerful
tyrants feared by all creatures, driven by greed, lust after treasure, greed colors their every scheme and plot, believe that the world's wealth belongs
to them by right.
The metallic dragons are described as pretty much the opposite, as inclined to actively oppose tyranny, lend a helping hand in unseen ways, befriend a lost
child, a wandering minstrel, or an innkeeper.
In particular silver dragons are described as:
Dragons of Virtue. Silver dragons believe that living a moral life involves doing good deeds and ensuring that one's actions cause no undeserved harm to other sentient beings. They don't take it upon themselves to root out evil, as gold and bronze dragons do, but they will gladly oppose creatures that dare to commit evil acts or harm the innocent.
Other Monster Manual Examples
There many more Monster Manual examples of good and evil creatures, particularly evil ones. Of interest might be the demon and devil entries, the hags, the incubi/succubi, and others.
Best Answer
Yes, there are several ways to get the Death Attack ability without being evil.
None of these options require the character to be evil-aligned.
However, it should be noted that Death Attack is, in many ways, even more limited than Sneak Attack:
This info was pulled from this list. I found it by Googling 3.5 "lists of stuff" "death attack" (expecting to find my answer in this excellent collection), but found the linked page instead, which was just as good. Next time you have a "what are all the ways to [do X] in D&D" type of question, try something like this - you might be able to answer your own question!