How can I install Ubuntu 'alongside' Lubuntu?

There is a dual-boot guide on the Ubuntu Documentation pages. You can replace the word Windows with Ubuntu, so that you end up dual-booting Ubuntu and Lubuntu.

1. When you reach the partitioner, select "Advanced Partitioning" or "Manual Partitioning".
2. You will get a list of the partitions on your system.
3. You need to have free space on your hard disk to install Ubuntu. So, there are two ways that you can free up some space. Either you delete some partitions (that you do not need any more) or you can shrink your existing partitions (so that some space gets freed up). I am assuming that you will shrink your partitions.
4. Select the partition you want to resize and click on 'Shrink'. If you are unsure as to which one to use, then I suggest that you resize your '/' or root partition, i.e., the partition that is mounted under '/' symbol. Select "Size:", press Enter. Type in a new size for your partition. It's recommended you free up at least 10 GB + your RAM size * 2 of free space for your Ubuntu install. Press Enter when happy with your changes. It may take some time to apply the changes.
5. Create a swap partition of at least twice the amount of your RAM (your RAM size * 2) (if you don't know, 2048 MB is a good value). To do this, select the free space, then click on 'Add'. Enter the size and then select type as 'Swap'. Press 'OK'.
6. Create a partition for your Ubuntu installation. To do this, select the free space, click on 'Add'. Select the type as 'Ext4' and the mount point as '/'.
7. Select "Finish partitioning and write changes to disk".
8. Continue with the installation.