It is not that the stall speed increases with altitude, the IAS decreases, thus approaches the stall speed. As altitude increases, the airspeed can approach Mmo, AND approach stall speed. The margin between Mmo and stall speed is the so-called "coffin corner." In a U-2, this margin is less than 10 KIAS at altitude. This does not give much margin for turbulence, or error. Turbulence is what is believed to have caused the loss of a U-2 between Japan and Korean approximately 5 years ago.
It is not true that Learjets have a "coffin corner" problem. In a Lear 35, the IAS at FL410 for example will be in the area of 210 KIAS, depending on the OAT. At a typical 15,000 pound weight, the Vref (clean) is 167 KIAS for banks up to 30 degrees, and 157 KIAS for banks up to 15 degrees. As you can see, the margin is approximately 43-53 KIAS. So, this is rarely a problem. One exception is where the AFCS (autopilot) is engaged in "altitude" mode, and severe turbulence including a strong downdraft is encountered. The AFCS will try to hold altitude by increasing the angle of attack, which at the same time will bring about an ever decreasing IAS. Now, this margin could possibly decrease to the point of concern. The remedy in this scenario is to immediately disengage the altitude hold, and request a "block altitude" from ATC. I have an excellent article on "coffin corner" written by Pete Reynolds, Vice President of Flight Test for Learjet (Bombardier), but it must be in my office, as I can not find it at home. I will post it if I can find it.
Check 6
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Kick the tires, light the fires, first off is lead, brief on guard.