Why does My '00 Buick Lesabre shakes when accelerating between 45 and 50 mph?

SOURCE: 1994 buick lesabre

check your tyres and wheel alignment and wheel balance if all that is good inspect your engine mounts for wear

SOURCE: 2000 Buick Lesabre runs like ****

Sounds like a bad spark plug or spark plug wire arching out causing an engine misfire.

SOURCE: 1997 Buick lesabre limited when accelerating, most

Here's a list.
Retorque throttle body possibly the gasket
Spark plugs
test coils
plug wires
throttle positioning sensor
map sensor
camshaft positioning sensor
timing belt? not likely
knock sensor

SOURCE: 1996 buick LeSabre runs rough at 50 mph

Sounds like low fuel pressure. i.e. fuel pump, fuel pressure regulator, or fuel filter.

SOURCE: 1997 Buick LeSabre, 54,000 miles

remove plugs and check for carbon tracing . if found plugs and wires will fix problem