Your life path number is 1 (birthday number) and your destiny number is 11 (name number). The resonance of those two major numbers may have been a predisposition for the originally seeing 1:11 on clocks more often than expected even when taking cyclic repetitions into consideration.

The time 1:11, because it contains repetitive digits, may have provided an inclination to see other numbers with repetitive digits.

The number 1 is a number of independence, investigation, and leadership. The number 11 is personal. The meaning always has to do with spirituality, 11 is the most spiritual number of all, but the meaning to you is likely to be unique. In your case, it seems to correlate somehow with the person you are thinking about as you notice the number.

Your friend may be been more affected by your disclosure than he expressed. There is a certain contagion about mystery. The unanswered lodges in the subconscious. The subconscious is effective regardless where conscious attention is at or what thoughts are in progress. When the environment contains something or a combination of things the subconscious is alert for, the conscious attention is directed there.

Your heart's desire number 8 (vowels total) tells me you have a strong need to be in control of your life.

I can not say with certainty what the clock times represent for you. The two strongest numbers in your numerology profile are 1 (your life path) and 11 (your destiny). I suspect the time 1:11 is the base from which the other repetitive sightings have manifested.

Also consider that the friend who is in your mind whenever you see the stated clock times is somehow identified with those times. There may be a clue to meaning there.