Perhaps you have a:
tail - which may be kept in hindsight.
I dared not to admit – I lied,
Tail sound like tale, something that may be told instead of admitting the truth. (Also, the last four words' initials give tail.)
So found “friends” on this trip.
If you got a tail, someone is following you.
My propensity to grip (sometimes), Or shoot out from the hip,
An animal's appendage from the hip, that if prehensile, can grip.
Or generosity with tips, Should keep heads down.
Tails showing on coins means heads are down. (Taking this as one clue, else just tails are long tips.)
#1 I'll likely leave it behind - you will outrun it.
#2 But I'm not an animal - not the animal type of tail.
#3 If you can't see it, you may be ahead of me - the tail is behind you.
Least confident of lines 1 and 5, but seems to fit.