Yes. Both poems ponder the nature of God. The two poems are often paired. Let's consider "Tyger, Tyger" first. Stanza are cited first; my analysis appears in brackets below each section:

Tyger! Tyger! burning bright
In the forests of the night,
What immortal hand or eye
Could frame thy fearful symmetry?

(The speaker wonders what sort of God could create something so "fearful"...fierce and yet wonderful.)

In what distant deeps or skies
Burnt the fire of thine eyes?
On what wings dare he aspire?
What the hand dare sieze the fire?

(What sort of a God would be bold enough and strong enough to forge such a fearsome creature?)

And what shoulder, & what art.
Could twist the sinews of thy heart?
And when thy heart began to beat,
What dread hand? & what dread feet?

(Not only is this God awesome, he is a consummate artist, beautifully crafting the tiger's sinewy strength. The power of such an artist inspires a dreadful, respectful fear in the speaker.)

What the hammer? what the chain?
In what furnace was thy brain?
What the anvil? what dread grasp
Dare its deadly terrors clasp?

(As he ponders the wonder of the tiger, the human speaker contemplates the methods of God. All of the questions will go unanswered. The power of God will be marveled at by man, but his methods never known.)

When the stars threw down their spears,
And watered heaven with their tears,
Did he smile his work to see?
Did he who made the Lamb make thee?

(The speaker, still awed by God's power, is left to further wonder how a God capable of making such a deadly creature could also make the defenseless lamb. Though it seems that he knows both were made by the same God, the dichotomy of the creation is mind-boggling.)

"The Lamb" considers the nature of man from the perspective of God's most helpless creatures. The speaker is comparing the helplessness of man to the defenseless lamb. Humans, he argues, like the lamb, are led and sustained by God alone. It is through his grace that we live at all. The repeated lines, "little lamb" are an allusion to the followers of Christ. In the Bible, Jesus is referred to as the "shepherd of his people" and also as "the lamb of God." By linking both the sheep and the shepherd, the speaker is saying that all of God's children experience divinity.

Does thou know who made thee,
Gave thee life, and bid thee feed
By the stream and o'er the mead;
Gave thee clothing of delight,
Softest clothing, woolly, bright;
Gave thee such a tender voice,
Making all the vales rejoice?
Little lamb, who made thee?
Does thou know who made thee?

Little lamb, I'll tell thee;
Little lamb, I'll tell thee:
He is called by thy name,
For He calls Himself a Lamb.
He is meek, and He is mild,
He became a little child.
I a child, and thou a lamb,
We are called by His name.
Little lamb, God bless thee!
Little lamb, God bless thee!