I like the one scene during Lion-O's anointment trials where he's cornered by Slithe on top the mountains. Tygra knows he's not allowed to interfere but does so anyway and saves Lion-O's life.
Snarf going all badass to save some random Unicorn in the episode "The Terror of Hammerhand". Also counts as a Moment Of Awesome for Snarf.
Both times that Lion-O was reunited with his father count in my opinion.
Any time Mumm-Ra shows compassion and love for Ma-Mutt. He even apologizes to him at the end of "Ma-Mutt's Confusion"!
Starts as a Tear Jerker. When Snarf (who feels he's becoming a load to the now grown up Lion-O) gets ready to return with his long lost nephew to his rediscovered home planet forever, the surprised but kind-hearted Lion-O doesn't give much protest before saying goodbye and that he will miss him - fighting back tears. It takes only a few moments from the ship's departure for it to land again and Snarf to jump back into Lion-O's arms.