The best way to connect a sub to an integrated depends on the available I/Os on both units. The OP specified that his LFD integrated has no pre-outs or sub-out. However, he doesn't mention which sub he's using or what I/Os the sub has.
Some subs have a single mono LFE RCA input. Some have left and right RCA inputs. Some have speaker-level inputs, some have speaker-level inputs and outputs. Some have stereo pair RCA inputs and outputs, which are useful with a tape or effects loop.
If you have a stereo pre-out pair and the sub has a stereo RCA input, use that. If you have a stereo RCA output but the sub only has a single mono RCA input, you can't fix that with a Y-adapter. You'd need a stereo-to-mono mixer of some sort.
If your sub has speaker-level inputs, use those. IME they sound surprisingly good and you don't have to turn the sub up as much, which should keep noise level down as well. I have found that--like anything else--the sound quality improves with better speaker cables. In other words, use something better than lamp cord.
Some subs have a single mono LFE RCA input. Some have left and right RCA inputs. Some have speaker-level inputs, some have speaker-level inputs and outputs. Some have stereo pair RCA inputs and outputs, which are useful with a tape or effects loop.
If you have a stereo pre-out pair and the sub has a stereo RCA input, use that. If you have a stereo RCA output but the sub only has a single mono RCA input, you can't fix that with a Y-adapter. You'd need a stereo-to-mono mixer of some sort.
If your sub has speaker-level inputs, use those. IME they sound surprisingly good and you don't have to turn the sub up as much, which should keep noise level down as well. I have found that--like anything else--the sound quality improves with better speaker cables. In other words, use something better than lamp cord.