The normal set up is that both motor and lathe (and often the countershaft- to increase the number of speeds available) carry stepped pulleys.
Often three sheaves on the motor pulley and three matching sheaves, but reversed, on the lathe spindle, for three speeds.
A countershaft with two stepped pulleys would increase the three speeds to nine. Even one stepped pulley will double the speeds available.
The speed will be determined by the number of poles in the motor. Usually single phase motors on lathes run at 1470 rpm.
Your picture shows a 1400 rpm motor. 45 watts is pretty weak motor, and not suitable for most lathe work (Unless you plan to use a watchmaker’s lathe).
Most single phase motors for lathes are likely be at least 500 watts
The motor speed for an AC is not variable, it is tied to mains frequency.
The speed of the lathe spindle is varied by changing the belt between the sheaves of the pulleys on motor and spindle.
CATCH 22
You might need to bore the pulley out, or bush it, to fit the motor shaft
And you need the lathe to do that! Plus the pulley will probably have, or need, a tapping for a grubscrew.
If you want to reverse it, you will need particular switchgear, and preferably, for safety, a No Volt Release switch between that and the mains.
If you are unsure, let someone who does know what they are doing wire it up!
(I’ve just made a cutter grinder, and reversing the motor requires a three pole changeover switch with nine connections, some interconnected!)
If you are wood turning remember that saw dust flies everywhere, more easily than metal. And some wood dust is corrosive (Oak for instance), so keep the machine clean!
You will be able to use the lathe to cut metal for your clock repairing, but the speeds needed will be different. And you will need measuring equipment.
Whatever use to which the lathe is put, you will need to ensure that the tool is sharp (Bench grinder for High Speed Steel. Doubt if carbide rips would be suitable for wood turning) And the tool needs to be mounted on the centre line, to cut properly, if at all.
Sounds like, as a newbie, you will need a lot of advice and help.
Where are you located, in case anyone is willing to give you face to face help?
Howard