Would be the odd man out in my mind.  Radke has too good of a track record to stink like this for an entire season.  Silva needs to get it together, and might have some value as a DP-inducer in relief, but I don't see him making that transition.  Lohse is young enough and talented enough (read: throws hard enough) to possibly succeed in the bullpen or draw interest from someone willing to take a flyer on pitching (Florida? TB? NY?).  

I'd replace him because if he turns it around they could get a prospect in a trade(not a great one). Liriano must be put in the rotation now.

Silva has to go.  I know he is finally getting a feeling for his sinker, but 15 homers in 8 games????  Baker should stay, with Liriano coming in, Radke and Loshe still.  I say get the old guys out if they are not producing so the young guys can get the experience.

Silva - 8 games, 2-6, 8.80 era, 13/4 -k/bb, 15 hr 46 inn
Lohse - 7 games, 2-3, 8.33 era, 21/18-k/bb, 6 hr, 35.2 inn
Radke - 8 games, 4-4, 7.57 era, 22/9 - k/bb, 11 hr, 44.0
Baker - 6 games, 1-3, 4.67 era, 24/4- k/bb, 5 hr, 34.2

but it really doesn't matter.  Both have been atrocious, and both have tossed decent outings of late--Silva on May 4th against KC, Lohse on May 10th in Texas.

Radke's been a bit better lately, and he has the experience & wit, I think, to turn things around, becoming a league-average pitcher.

What I'd do:  callup Boof Bonser and give him & Liriano some favorable starts.  Look for outings at home, or outings on the road against below-average offenses in pitcher's parks.  (Confidence does matter in this game.)  In the meantime, don't screw up Santana, Baker & Radke's rest days, but at least begin to work the two of them into the rotation.  If unfavorable starts arise, throw Silva or Lohse--whoever--to the wolves.

(By the way, "whom" is the subject of your title sentence; as a noun, wouldn't "who" be the proper usage.  I'm no grammatician, so disregard if you grew up in the Canadian school system, in which case I'd clearly be in error.)

1. Lohse isn't a free agent after this year. He is still in arbitration.
2. Lohse is second on the team in quality starts after Santana. Including his last one. Why would you replace him now?
3. Radke will likely retire after this year, so if you are ready to put Liriano in the rotation and play for the future, he might well be the logical candidate.
4. Silva has struggeled with his sinker and that might be something he can work on better pitching more often out of the bullpen. On the other hand, he had a very good outing before his last one so you also might want to give him another shot before going to plan B.
5. Liriano is probably only good for 60-75 pitches. He might make it 5 innings as a starter, but he would have to get outs more efficiently than he has to do that. So you probably are going to need to plan on someone in the bullpen to give you two or three innings to get you to the 8th when you would normally want to plan on turning it over to the bullpen. And there is no guarantee Liriano won't struggle the second time through the order.
   

it's moot now... according to rotoworld, liriano will take over for silva starting this friday against the brewers.