Do you have a .INCLUDE XXXX.yyy on the schematic? XXXX.yyy is the name of the Lib you downloaded. The Lib must be in the same directory as your schematic, or where LTSpice puts its own subcircuits (On my installation it is C:\Program Files\LTC\lib\)
OPen the lib file inside LTSpice and check that it has a .subckt 74hc02 line somewhere in it.