Join the sentences into one simple sentence: Do or die. Live and let live.
There are many ways combining these sentences can be accomplished. In my mind, the most direct way would have to rely on the concept of the compound sentence. The compound sentence combines two or more independent clauses into one with the use of some type of punctuation. Given how both sentences featured in the example are imperative sentences, this can be played with in a variety of ways. For example:
"Do or die, or live and let live."
"Do or die, and live and let live."
This is how I see that you are able to combine both of the sentences into one direct sentence. However, as you can tell, the challenge here is that both of the clauses' meanings are opposite of one another. To "do or die" means compliance or death, while the idea of tolerance and permissiveness is a part of "live and let live." This makes both of them contradictory to one another, so if you combine them in one sentence. It will seem a bit awkward in terms of meaning. so you might need to add some more words in order to bring out their divergent meaning in one sentence:
"Do or die" was one choice, and "live and let live" was another.
Adding some words to bridge the opposing meaning of each sentence, I was able to add a comma and the conjunction "and" to make a compound sentence.