One clear advantage of the SQ lounge over the other two lounges is the location. Usually, LX flights will depart from one of the "wings" of the terminal, so the SQ lounge might be right next to the departure gate or at the other side of the terminal root, but there's a shortcut that doesn't require you go through the Duty Free shops. The other two lounges are at the end of the terminal "trunk" and would require you to walk a considerable distance back to the root, so I would always recommend the SQ lounge. It's actually not too bad, unless you don't like an attended bar over serve-yourself alcohol (which is only available in the first class section). I particularly like the relatively efficient pager system for shower reservations.

Edit: Even though you should also be able to use the Plaza Premium Lounge (also at the terminal root), I wouldn't bother. Last time I passed by, there was a huge queue in front of it, and from what I've heard, that lounge must be really bad and usually overcrowded, as it's a pay-in lounge used by most people who don't have lounge access otherwise.

Other than that, if you plan on visiting The Bridge on your outbound, be sure tom choose the right part of the lounge. To the left, you'll find a relatively quiet semi-dry area (only wine until 5pm) or a much more frequented part on the right hand side, which features "The Bakery" with a really good food selection, and the main bar, where they'll serve alcohol all day. I would always recommend the right hand side unless you want to have a really quiet environment.