Check earth riders.com they have the trail maps. I have not been over to Lawrence in years, but I love it every time. A couple of my co-workers drive over ever other week. THey like the river trail, but I have always gone to the lake. I hope you get a chance to ride it
I did the half ironman they had in June and the roads out by Clinton lake are great for biking. When I was pre-riding the course, I had maybe two cars pass me in the two hours I was out. I stayed "downtown" and it was about a 15-20 minute drive west of town.
2014 Pivot Mach 5.7 MTB, 2009 Chris Boedeker custom, 1988 Tommasini Prestige, 2007 Bill Davidson custom; 1988 Specialized Stumpjumper
As noted above, could be sunny - could be icy.
One of the standard rides in the Lawrence area is to ride out to Lone Star Lake and back from town. I think bikely.com or mapmyride.com have the route. Variations of this ride would take you over the dam at Clinton Reservoir.