During the Lubuntu installation you will have a window labelled Installation type and you will have your partitions showing in the main window. Below that you should have several tabs, Add, Change Delete and below that Device for bootloader installation. Click the down arrow to the far right of the tab just below and you should see all the options.
As far as the partition to install to, if you have an existing partition you want to use, click it to highlight it in the main window and then click the Change tab. You will get a new window where you can select the mount point for the system which should be /, which is root. Click the down arrow to the right of Mount point box to see options.
I always use Manual, Advanced or in the current Lubuntu Something Else option. If you don't see those options it may be because you selected the Install Alongside option. I've never used that so I don't know what the options are.