Can Lenovo Vibe S1 use PC's internet via USB cable (without using Wifi)?

What you are trying to do is called Reverse Tethering. For achieving the reverse tethering you will need to have a reverse tethering tool compatible with your device. Follow the below mentioned steps to connect your smartphone to your PC and get the PC internet on your device via USB cable -

Requirements
1. Proper drivers for your device.

2. Reverse tethering tool.

The XDA developers have a good Android Reverse Tethering Tool. You can download it from the link http://forum.xda-developers.com/showthread.php?t=1371345 .

Here are the steps you need to follow. Please note that this tutorial assumes that your device has root access. If you are not rooted, you won;t be able to use this method.

1. Connect your device to the PC using USB cable.

2. Turn the USB Debugging ON. On most of the devices, the path for doing so is Settings > Applications > Development > USB Debugging > Turn On.

3. Download and install the Reverse Tethering Tool indicated above.

4. Launch the tool downloaded above. Choose your device from the Select a device drop down list.

5. Choose the DNS from the drop down list DNS to use. Please do not use 198.168.1.1. You can select any other DNS. The tool may select an appropriate DNS on its own.

6. Now click on Connect button on the tethering tool.

7. The tool will install the required apps/files on your phone. Accept if you get any prompt to install any app.

8. Grant permission to use root permissions.

9. The tool on your PC should indicate you that it is connected.

That's it. You can now use your PC internet on your Android.