In Of Mice and Men, why does George say that they can’t let Lennie escape to live on his own?

The short answer is that Lennie cannot survive on his own.
In chapter one Steinbeck describes Lennie as a "bear", with with "huge paw(s), and as a
"snorting horse".  These images are meant to convey wild and unharnessed power
suggesting that Lennie operates on simple instinct, not reason.  This impetuousity is
often hazadous.

When George and  Lennie arrive at water
source that had the potential to be stagnant,  George demonstartes caution while Lennie
plunges into the water and drinks deeply even though this made him ill only a few nights
before.   Lennie's instinctive reactions are often dangerous to others as well. One need
only consider his history  in Weed, with various pets, in mangling Curly's hand, and
killing Curly's dead wife.

The dream that held them
together died in the barn with Curly's wife. George could not watch over Lennie anymore.
Certainly not while on the run from the authorities.  Yet, without constant supervision
Lennie was a danger to himself and a threat to others. Without George to care for him
Lennie would undoubtedly experience and create great suffering before facing his own
inevitable death. Candy once confided to George that he regretted allowing another man
to put his down his old dog. Similiarly, George felt it was his job to put Lennie down
in the kindest possible way for George's good, his own good, and the good of others. 
George's act is the highest form of mercy.