This is a great question! Yes, Lear's language changes as his character undergoes changes. The language reflects internal changes as you suggest, and these internal changes are also reinforced the physical changes Lear also undergoes.
As Lear moves from the courtly life of pomp and circumstance that he has known his whole life, to living at the pleasure of his daughters, to actually being abandoned on the heath in the midst of a violent storm, his speech does indeed change.
The most basic change he makes is from verse to prose. In the first Act of the play, Lear is the King in every sense of the word and his language reflects his exalted state:
Know that we have divided
In three our kingdom; and 'tis our fast intent
To shake all cares and business from our age;
Conferring them on younger strengths, while we
Unburthen'd crawl toward death.
Lear, in the above text from Scene i, gives out his plan, but does so in the most formal of royal ways, by referring to himself in the plural as "we" rather than "I." Kings spoke in the "royal we" because they weren't just speaking for themselves but for their countries. Lear is certainly in his full-on royalty in this opening scene.
Later, in Act IV, Scene vi, he speaks in prose, language reserved in Shakespeare's plays for low-born characters, casual conversation and characters not in their right minds.
Look with thine ears. See how yond justice rails upon yond simple thief. Hark, in thine ear. Change places, and handy-dandy, which is the justice, which is the thief?
Even in these "mad" scenes, when Lear speaks in verse, it is jumbled, unconnected thoughts:
Now, now, now, now,
Pull off my boots. Harder, harder. So.
This speech is definitely meant to reflect his confused and "mad" state of mind.
At the end of the play, the verse he speaks to Cordelia is less pomp and circumstance and more lyrical imagery. This is a nice reflection of the feeling for life that he has gained:
We two alone will sing like birds i'the cage.
When thou dost ask me blessing, I'll kneel down,
And ask of thee forgiveness.
Shakespeare definitely uses the rhythm of the verse and the addition of prose text to give the audience (and the actor performing the role) clues about Lear's state of mind throughout the play.