What makes such lines so memorable? How can I create my own?
An original twist with resonance, often combined with poetry, concision.
The "twist" is a surprise, but resonates with the sentiment. "Tears in the rain" has a twist: We see tears, but "in the rain" they vanish away; meaning a person is crying and expressing grief in public (outside, obviously) but nobody else knows. This is a poetic, concise way to express this feeling we sometimes have of private grief we hide from others.
Live with Honor, is the first part, an easy instruction, pablum really, because every normal person would like to believe they live with honor. Die with Glory is the twist in the command, but it resonates: The opposite of "living" is "dying", usually a tragedy. But now part of living with honor includes the courage to die, and not by running from it but by embracing it. Very few of us want to do that! But we expect our soldiers to be courageous and put their lives on the line; so this aphorism is for the elite that risk their lives; the twist resonates with (adds meaning to) the first part.
"Make My Day," by Dirty Harry, encouraging a criminal to draw on him, so he can kill him. This is just the twist: In the context of this scene, the twist is that in a dangerous situation Harry expresses the opposite of fear: He doesn't fear a shootout, he is eager for it, because it would give him an excuse to kill a criminal and he would enjoy that. None of that is in our conception of an ideal cop, so this is a twist on those expectations. And it resonates (or anti-resonates) with that ideal perfectly for the title character, Dirty Harry.
On top of that, "Make My Day" carries the connotation that even if Harry did kill the perp, he wouldn't care that much, he'd be happy for a day and forget it; on to kill the next crook.
That is why "Make My Day" would be better than "I Dare You".
It helps to have poetry. Not in the rhyming sense necessarily, but notice "Live With Honor" and "Die With Glory" are poetic choices, the same number of syllables with the same stresses, "Live/Die" are opposites, "Honor/Glory" are not opposites but are often used together elsewhere. (They are opposite in the sense that Honor feels more passive and Glory feels more actively heroic).
Related to poetry is concision; being brief. Poets can pack a lot of meaning into a handful of words. Concision is critical to a catch-phrase. Not at the expense of clarity, but the shorter the message, the more punch it has. The typical conversational speaking rate is 2 words per second (2.5 in some cultures / cities, like NYC, 1.5 in other cultures / cities, like the American South).
So as a rule of thumb I'd say your catch phrase should be six words (3 seconds) or less, perhaps seven words. There are studies, in advertising, on the efficacy of slogans and on the words in a headline for an ad or letter. Studying just the number of words, these droop when going from six words to seven, and drop off dramatically going from seven to eight words. There are some exceptions that may be related to poetics (rhyming, rhythm, single syllable words). But as a rule of thumb, keep it short and sweet. And, of course, it should be easy to say, a tongue twister is not a good catch-phrase; and it should not require any thought to understand it. So a puzzle or double entendre is probably not a good catch-phrase if the dimmer half of us might not get the joke. (You should certainly use those elsewhere in dialogue, just not as your iconic phrase.)
Inventing a good catch-phrase is worth weeks of work, which may seem odd for a six word phrase, but in some works, that catch phrase becomes iconic, and the one thing readers take away verbatim from your writing, that means only your writing. If it is good and people use it, it can become a free advertisement for your work.
If your story can use one, it is worth working on.