It is not betraying any great secret to reveal that the M62 was meant to end in central Liverpool. The question is what the exact route would have been and where it would have ended. This page will try to answer that question. Click any image to see a full size version.
A document produced by Liverpool's city engineer in 1974, two years before the section between the M57 and the current terminus opened (which suggests it was published as construction began on this part), confirms that the M62 should have ended on the never-built LIM.
The obvious reason that the M62 was never finished is that the LIM was never built, though the document does outline at least one option to allow completion of the route independently of the LIM.