It is essential to put the play into context. Integrate comments on context into your explanation of language/performance.
The political world had been a time of uncertainty. This site has extensive commentary on the background to King Lear. Don't be put off by the enormity of it! At the other end of the spectrum, if you want a very brief overview, look at Sparknotes.
When it comes to context (depending on your own question) consider politics, social change, justice, religion, madness and death and disease.
The language in King Lear shifts from formal, ceremonious register to informal and conversational. It is a times bombastic and at others restrained. All is used to intensify the dramatic effect upon the audience.
Lear's language is commanding. Even when he's dividing the country his language shows he is very much in charge. Even in the storm he tries to command the elements.
There has been great debate about whether or not King Lear is a religious play. Despite the pagan setting, it is full of Christian terminology. Learning through suffering is a Christian lesson.
The imagery of Cordelia's death could be associated with the pieta. There are prayers, oaths, sermons and parables (The Fool often gives little homilies).
There is distinct poetic imagery in the language: it is vivid and emotive. Again, Christian imagery creates complex links. References to classical mythology contribute to this complexity.
There are clusters of images that repeat through the play: blindness, animals and disease.
Antithesis is used linguistically, perhaps to reflect the conflict in the play. Repetition and lists are used. What is the dramatic effect of using these devices on the audience? Have a look here for more guidance on imagery.
Verse and prose is used unconventionally. Sometimes prose would be used to reflect the status of the character. Conventionally, low status characters speak in prose. However, Gloucester and Edmund are high status, but speak in prose in 1.2. Although high-status, Lear sometimes speaks in prose, particularly with The Fool and Poor Tom. Why might Shakespeare do this? Does it reflect his common humanity or his lack of status? The verse is mostly iambic pentameter (which he would have learnt at school). He's quite experimental in King Lear moving away from end-stopped lines and using caesura and enjambment. Why?
If you fancy signing up to enotes, have a look there. Here is an interesting article. Here is a famous essay. This is good! There's even a quiz.
Look though other posts on this blog for more handy links!
Let me know if you have any problems. Nearly there.