How do you punctuate an if/then when both the "if" and the "then" are implied?

You could use a colon to separate the two short sentences, because you are stating the antecedent and then the logical conclusion of an implied if..then rule, completing a "Hypothetical syllogism" by affirming the consequent having posited the precedent.

This would be a use of the "syntactical-deductive" use of a colon to introduce the logical conclusion of the fact stated before the colon. To me, in written English the colon makes it more clear that you are making a conclusion based on an implied If..Then rule.

The implied if..then rule is the major premise, called a "conditional proposition" that is a statement that has an antecedent and a consequent. (If [antecedent] then [consequent]). The minor premise is a categorical proposition affirming the antecedent. By "modus ponens", the consequent is a logical conclusion of the antecedent. "You lie: you're out." The three statements form a "hypothetical syllogism".

You could also reverse the negatives of the sentence, as in "You're not You could also reverse the negatives of the sentence, as in "You're not out: you didn't lie", by "modus tollens".

For the other example "I like it: I don't love it", there isn't a clear implied If..then rule. The syllogism would be an example of a disjunctive syllogism, where the major premise is a disjunctive proposition stating disjointed alternatives and the minor premise is a categorical proposition about one of the alternatives. This gets shaky when the alternatives are not mutually exclusive: you don't have a true disjunctive proposition. A person could both like something and love the same thing. Therefore stating or denying one of the alternatives doesn't have a true conclusion. The two statements are independent and should have a semicolon. "I like it; I don't love it." (two independent facts). "I don't love it: so I don't like it" does not make sense because to most people it is not a true categorical proposition that "You can either like something or love it".

I like it— I don't love it.

You lie — you're out.
The Punctuation Guide

I prefer the "em" dash for the described examples.
The examples probably should not be used in formal writing, except to report what somebody has said, or when attempting to get the reader's attention.

The above cite from The Punctuation Guide does not allow for the use of a "em dash" to replace a semi-colon. Generally it can replace parentheses:

I like it (I don't love it).

You lie (you're out).

That works for the first example, not the second.
I am stuck on the "em" dash.