Whenever I'm looking at a trade, I check a couple things.
on google do a site:url.com to see how many pages G has included in it's database. If there are very few pages, or none, that's a sign there may be a penalty for something and may want to stay away from.
Then I check the DA/PA. Moz has a nice little chrome plugin to do that when you hit the page.
Majestic also has a chrome plugin to let you see the backlink summary for free, or if you have a membership can see a lot of the most needed info from the browser bar.
Then of course you want to look and see where your link will end up at, and how many more offlinks there are on that site.
With LS there are a ton of trades to be had, you just have to watch out for the really spammy ones and stay away from them. I noticed that a lot of the traders there run the footer/blogroll trade links all the way thru their sites, which makes them look spammy to G, so best to stay away from them also. If you find one of those that looks good otherwise, message them and ask for a link inside one of their posts which would then just show up on that one page.
Even lower quality sites can offer a spot to change up the "anchor text" for your link. I also find a number of blogs on LS which have comments turned on and many of them don't monitor comments so you can use it to get free links from comments. Even if they are no-follow, G likes to see a mix of follow/no-follow in your backlink profile to make it look less spammy
Good luck
