Linux Lubuntu won't connect to Wi-Fi?

Hmm, sounds like a driver issue. Look online for the wireless card drivers for your specific PC, and make sure they are for ubuntu. You will either need to use a different pc and transfer them to the ubuntu machine via flash drive, or plug in the ubuntu pc directly into an internet router/modem through ethernet.

I had a similar issue when I first booted ubuntu 12.04 on my MacBook Pro. I connected it via ethernet and ubuntu automatically found the drivers and installed them.

Don't forget to enter the SSID and Wi-Fi password - even if your Wi-Fi device is working (which it very likely is, with a Lenovo on Lubuntu), the device still needs the Wi-Fi details to be able to connect.

Austin advice is good - you can check if there's a driver missing by using Administration/Driver Manager.

This sort of stuff will get fixed during the install if you make sure the machine has an internet connection (wired if necessary) while installing.