Learn English – “I should have let you known”

This is an example of elision: a process of omission of words which are to be inferred by the listener. Elision happens in many languages, and follows certain patterns.

For instance, in English, as in many languages, a brief answer is possible, like this:

Q: Where did you go?

A1: To the park. [Subject and verb are elided.]

A2: ? Park. [Possible, but less usual, and creates an abrupt sense. Perhaps the speaker is out of breath, or indicating an emotional state of being disinclined to conversation.]

Q: What did you have for dinner?

A: Pizza. [A one-word answer to a "what" question is not unusual, and not considered abrupt. "Steak" is the direct object of the elided sentence "I had steak for dinner", where there are no prepositions on the word.]

In the sentence:

Nothing the god of biomechanics wouldn't let you in heaven for.

words are elided from the hypothetical sentence "They (= those things that I did) were nothing the god of biomechanics wouldn't let you in heaven for."

By the way, a better preposition in this type of sentence, at least in a more formal setting, would be "into". If there is no complement for the preposition, it is just "in":

Let me { in | *into }.

But with a complement like "building":

Let me { in | into } the building.

Using "in" for "into" is acceptable, but at the cost of contributing to an informal, conversational tone to the sentence (which is obviously appropriate in the context here). This view is probably due to the the bias arising from everyone having had it drilled into their heads in elementary school that "into" should be preferred.

In any case, that would be the only nitpick I could possibly have with the sentence; not its elided subject and verb. :)

The present perfect conceptualizes the past thing from the point of view of its relation to the present.

Having eaten pumpkin pie, I know what it tastes like.

My present knowledge is the result of eating pumpkin pie at some point prior to "now". The eating might have taken place 1 second ago or 1 year ago or 10 years ago. I might have some unfinished pie on a plate in front of me. All we know from the tense is that I am someone who ate some pumpkin pie at some time in the past.

With "having lived", if you said this and only this:

Having lived in India, I am familiar with the cuisine.

all that can be concluded from the statement is that you lived in India at some period in the past. It could be last week, or last year, or for the past 20 years. You are a person who can truthfully say "I lived in India". You might live there still.

Now, let's see if we complicate things by adding "all my life".

Having lived in India all my life, I am familiar with the cuisine.

All my life does not exclude the present moment; nor does it necessarily include it. You can easily say, as someone who has emigrated to Antarctica, "I lived in India all my life. But now I live here at the South Pole. Aren't the freezing temperatures refreshing?"

So, we cannot conclude from the statement whether you are living in India now, or have moved elsewhere. All we know is that you are a person who can claim to be someone who, at some time in the (recent) past, had been living in India since birth. all my life does not exclude the present but it does guarantee it: a person who had been born in India and who had lived there until very recently, could say "Having lived in India all my life..."

So, yes, you can say "having lived" whether you have moved away, or you still live there.