Concerning these two companion poems by Blake, the idea of experience in Blake's "The Tyger" can be thought of in contrast to the innocence of "The Lamb."
The narrator of "The Lamb" is a child who sees only the purity and innocence of the lamb, and by extension, nature. The narrator of "The Tyger" knows better. There is another side to nature (and this narrator is aware of it), just as there are two sides of the human: the innocent and the experienced.
Since the same being makes both, that means there are both innocence and experience--both lamb and tiger--within the creator as well. All creatures contain elements of both lamb and tiger, as does the creator.
Also, as is usual in Blake's collections Songs of Innocence and Songs of Experience, to which both of these poems belong, Blake is dealing with different perceptions of the same thing. In the case of these poems, he presents two different perspectives of nature, which by extension may suggest different perceptions of humans and the creator.
For specifics, look at the images created in "The Tyger." The tiger's symmetry is "fearful"; "dread hand" and foot; "deadly terrors." And notice stanza five: the stars cast down are an allusion to Satan being cast out of heaven, and the speaker asks if the creator that fought and won the battle for heaven, then looked at what he had created in the tiger, and smiled.
The creator of the tiger is no innocent. But the same creator made man, so both the creator and man have two sides as well.
The lamb and the Tiger represent two rather contrary aspects of divinity and also of the human soul itself, as hinted by the sub-title of Songs of Innocence and Experience.
Blake creates a binary of the lamb and the tiger like a thesis and antithesis where one represents mildness while the other a certain kind of ferocity. This binary, I think however, is not sufficient to reveal the nature of the Godhead and this is exactly what Blake implies as a synthesis of the two. But, this synthesis is not non-problematic at all. Like Swedenborg and Boheme and other mystics, Blake also sees God as two faces of the same force, like Boheme's light and heat, both coming from the sun. But, Blake suggests a beyond to both in an inter-fusion of the two.
The Lamb stands for the state of innocence while the Tiger, for that of the dark world of experience. These two are not part just a linear temporal continuum. They are intermeshed. as C.M. Bowra famously says about the tiger, in the cosmic hour of crisis and darkness, the tiger is supposed to revive the reign of innocence.