The LFE channel is a specifically encoded channel. There can be plenty of low frequency content in the other channels, though, and there often is. But that is not "LFE"; it's simply "low-frequency info that is encoded in the other channels".
When an AVR is configured as having a subwoofer, the LFE channel info is routed in its entirety to the AVR's subwoofer pre-out. The low frequency info present in any other channel is subject to the bass management configuration of the AVR. If a channel is set to SMALL (or is being 'crossed-over') then any frequencies below that channel's crossover setting will also be sent to the AVR's subwoofer pre-out.
Certain low frequency content is often mixed simultaneously into both the LFE channel and another channel (or channels) in order to provide some coherency to the mix as well as some directionality to the effects. Very rarely will all the low frequency information in any particular effect be mixed solely into the LFE channel. It is almost always shared or spread across the LFE channel and some other channels. How any particular low-frequency information will be reproduced upon reproduction, no matter where it is encoded, depends upon the end-user's bass management configuration.
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