LFE does not equal subwoofer
Dolby Digital programs may include a bass-only LFE channel, but this channel does not correspond directly to a subwoofer output.
It is possible for a program to contain an LFE channel, but a decoder may provide no subwoofer output because all of the bass information in the program, including the LFE channel, can be reproduced by the main speakers.
The opposite is also true: it is possible for a program to not contain an LFE channel, yet a decoder may provide a subwoofer output because some or all of the main speakers are unable to reproduce the bass information in the program.
The difference between the LFE channel and the subwoofer output is that the LFE channel is used to carry additional bass information in the Dolby Digital program while the subwoofer output represents how some or all of the bass information will be reproduced.