Well it could be a router issue. I read reviews HERE (which had some problems) & also a couple on the 3 com card HERE & also HERE

But then, if it is LW or LW is the catalyst for setting off the problem then I can make some suggestions.

Go to LW's Tools>Options>Speed & tick disable Ultrapeer Cap. & press apply button.
Set both uplds & downlds to autoclear.
Close all LW windows you don't need open at that time.
Reduce uplds to about 70-80% or more. Reduce downlds to 80 or 90%.
Whilst LW is open, click on top of the Progress bar so all incomplete files are organised by % downlded. Then select 1st at 0% & scroll down to last & select it whilst holding down SHIFT key also all at 0% are selected, then pres the Stop button. Then go to your incomplete folder & view it in list mode & click on size column so all are arranged by size. Now delete all those at 0 KB. This will speed up opening of LW & reduce stress on connections & hopefully your router.
You might also consider reducing shared files if you have multiple thousands of them. Good luck. Sounds like your comp is losing communication with your router b/c it's too busy.

Also don't use the Resume button on all incomplete files. This will also stress LW & your comp. If you use Resume/Find sources then just apply it to a couple or so at one time.