Simple question with more complicated answer. I assume you mean solo as apposed to traveling in the peloton of racers or, say, descending a mountain (when riders will hit 65 mph+).
Looking back to the last TdF that LA competed in his average speed for the prolog stage of 19km (11.8 miles) was over 54 kph (33.5 mph).
Looking at a longer time trial stage, he won the 55km (34 mile) stage at an average speed of 46.4 kph (28.8 mph).
Now these are averages over a certain distance - if he needed to simply max out speed you could shorten the distance further for some increase in speed. Let's just say 35mph+ shouldn't be too difficult. Could he break 40 mph unaided on the flat? I'd say based on these figures it's pretty likely even if just for a short time.
Fast huh? This is true. Track cyclists like Marty Nothstein hit well over 40 mph. The world record for the kilometer is 58 seconds. So you can calculate the speed from that, imaging that is from a standing start. The world record for a 200 meter flying start is about 9 seconds. Using these times and multiplying to the equivalent of 1000 meters comes out to 9 x 5 = 45 seconds for the kilometer which is 0.625 miles. That works out to 72 seconds for a mile. Now take 60 minutes (1 hour) and convert it to 3600 seconds and divide by 72 seconds to get the mph. Answer is 50mph!! Wow! That is a cyclists top average speed over 200 meters. Logically, a sprint specialist could hit slightly above 50mph when he hits the line. Say 52mph! Lance is not a pure sprinter. He is a road and time trial specialist, so his numbers are probably 5% lower.
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Depends on what kind of road he's riding on. If the terrain is flat and he's in a group the speed could anywhere between 20-30 MPH, if it's a descent he could be up to 50 MPH. On a climb OTOH the speed could easily drop to around 10 MPH on a really steep climb.