Is Beowulf the ideal epic hero? If not, what is he lacking?

Yes, Beowulf is basically the ideal epic hero. He is larger-than-life, exceptionally strong, brave, loyal, and respected. He does eventually fall in the battle with the dragon at the end of the poem, but he does so protecting his kingdom. The response of his men after his death shows that they hold him as a great king and hero.

Beowulf is not immortal, but he is "larger-than-life," meaning he is better than normal humans. He...

Yes, Beowulf is basically the ideal epic hero. He is larger-than-life, exceptionally strong, brave, loyal, and respected. He does eventually fall in the battle with the dragon at the end of the poem, but he does so protecting his kingdom. The response of his men after his death shows that they hold him as a great king and hero.

Beowulf is not immortal, but he is "larger-than-life," meaning he is better than normal humans. He is the strongest warrior we see in the poem. He is the one who defeats the dreadful monster Grendel, who terrorized Hrothgar's kingdom for years; none of his warriors were strong or brave enough to defeat the beast. Beowulf is so strong he rips Grendel's arm from his shoulder. 

Beowulf's bravery is also legendary. He chooses, of his own free will, to travel to Hrothgar's kingdom after hearing the reports of Grendel's ongoing violence. He puts his life on the line to help people in a kingdom in which he does not even live. He is brave enough to wait for the monster to come into the mead hall and fights him without weapons, as Grendel will not be using any. After killing Grendel, Grendel's mother starts taking revenge on the kingdom. Beowulf volunteers to go to the underwater cave to fight her on her own turf. He does need the help of a magical sword to defeat Grendel's mother, but that supernatural force may indicate that Beowulf is favored by the divine. 

Finally, Beowulf is a loyal and respected leader. His men trust him and swear allegiance to him in the fight against Grendel. Beowulf, in turn, asks Hrothgar to care for his men in the event that he is killed in battle. He becomes a respected king later in the poem and puts his life on the line again in order to kill a dragon that threatens his people. One of his men jumps in and helps defeat the dragon in battle after Beowulf is mortally wounded because Beowulf inspires loyalty in his men. They memorialize him after his death in a way that shows how lauded he is as a leader. 

One possible negative quality is that Beowulf is not completely selfless. He does take treasure from the monsters' caves, and he probably takes on the epic tasks to enhance his reputation and experience the glory of his victories. However, one could also argue that swagger and confidence are necessary in an epic hero. All in all, yes, Beowulf is an ideal epic hero.