The lathe carriage is the assembly that moves the cutting tool along and across the workpiece. It is made up of several parts working together: the saddle, the apron, the cross-slide, the compound rest and the tool post.

Role of the saddle:

• The saddle is an H-shaped casting that straddles the lathe bed and slides along the bed guideways (ways) in the longitudinal direction.
• Mounted on top of it is the cross-slide, which provides transverse (in-and-out) tool motion, and above that sit the compound rest and the tool post that clamps the cutting tool.
• Therefore the saddle's job is to support and carry the cross-slide and tool post, which is exactly the correct statement.

Why the other statements are wrong:

• The lead screw is not moved by the saddle; rather, the lead screw (or feed rod) drives the carriage through the apron mechanism during thread-cutting or automatic feed. The relationship is the reverse of "moves the lead screw mechanism".
• Spindle speed is set by the headstock gearbox/pulleys, not by any part of the carriage, so "controls spindle speed automatically" is incorrect.
• Rotating the workpiece against the tool is the function of the headstock spindle and chuck; the saddle only positions the stationary-but-fed tool.