Even if he though Johnson would be the best leader, there was no chance he could have won the election, which in the states typically comes down to Democrat vs. Republican.
So, a vote for Johnson was (indirectly) a vote that favored Trump.
Not in Illinois it's not.
Illinois is a Blue state. It was obvious that Clinton was going to win Illinois, so there was no need to vote for the candidate whose underlying philosophy you disagree with in order to prevent Trump from winning. Illinois voters who voted for Johnson did not contribute to Trump winning the election because Clinton won Illinois. If every voter in Illinois had voted for Clinton, it would have had absolutely no effect on the outcome of the election because Illinois electoral votes went to Clinton. As it is, Clinton got 56% and Trump got 39%.
Illinois has 18 Representatives: 11 Democrats and 7 Republicans.
Two of the republicans ran unopposed as the Democrats did not field a candidate.
Another, (LaHood) is the son of Ray LaHood, a moderate Republican who previously represented the district and was also Obama's Secretary of Transportation. I no longer live in Peoria, so I'm not all that familiar with the younger LaHood, but from his Wikipedia page, it appears that he is fairly moderate and has not been a Trump cheerleader. On a personal note, my wife thinks very highly of the senior LaHood. His office was instrumental in arranging an honor guard for my father-in-law's funeral. (Retired Air Force sergeant who served in Korea and VietNam) The younger LaHood defeated a Breitbart editor in the primary.
My point is that sometimes a district's voters have connections with their representatives that transcend politics. They see them as people/individuals first.
It's also good to remember most people in Illinois expected Clinton to win the presidency. Therefore, the idea that they needed vote for an opposition candidate they disagreed with in order to keep Trump in check would not have occurred to them. Since they expected a Clinton victory, they logically would have expected to rely on Congress to keep her in check instead.
I also voted for Gary Johnson, mostly to support a third party. (I don't vote a party line for either party. To quote Richard Pryor in Brewster's Millions: "Vote None of the Above.") I don't recall who I voted for for Congress, but I'm pretty sure it wasn't Rodney Davis (R) because I was in the mood to vote against incumbents that day.