Coming south on the Lake Washington trail I usually continue out the entrance to Gene Coulon Park and turn right on Park. I follow that to 6th where I make a right and go over to make a left on Logan which I ride to the airport perimeter road, an obscure right immediately after the bridge over the Cedar river. (An alternative is to continue straight on 6th through a Boeing parking lot after crossing Logan. You pick up the perimeter road at the back of the parking lot in the form a bridge off to your left crossing the Cedar river .)
Park, Logan and (to a lesser degree) 6th all can have a lot of traffic – and during the road construction in Renton they are likely all closed to traffic anyway.
Instead, when leaving the park one can go left across Lake Washington Blvd at the railroad tracks to get onto Houser which has bike lanes. After the warehouses you make a right on 8th and find the bike path on the south side of the street. You go left at Garden and at 6th you make a right and ride over to Logan, etc.
If you are heading for the Cedar River trail you can just stay on Garden until Bronsden and Liberty Park where you’ll find the trail by the Library. (Eventually there will be a trail between Gene Coulon Park and the Cedar River trail.)
If you are heading for the Interurban trail you want to stay on Garden until Bronsden and Liberty Park. Make a left onto Bronsden and continue on 2nd when Bronsden splits. Continue on 2nd for three blocks and then make left onto Burnett. After the park blocks, when Burnett ends, follow the curve around to the right onto 7th and ride the rest of the connector to the Interurban.