Although you can go about it the way you are doing, this is not really taking advantage of the pre-configured TKL appliances.

TKL isos (or VM images) are fully configured standalone complete appliances. You cannot stack them on top of one another like I think you are suggesting (although perhaps I misunderstand).

Core is provided as the base TKL system (or lowest common denominator) that all other appliances are built on. I see it as a development base for building/testing your own appliances. You would be much better off starting with either TKL PDC or TKL LAMP as the base of your system. I would suggest starting with the PDC appliance and installing LAMP components (from the standard Ubuntu repos). I would suggest this path as from my experience LAMP config is more straight forward than PDC.

Probably the easiest way to acheive LAMP and PDC would be to install them as two separate TKL VMs. Alternatively, if you are installing to hardware (rather than VM) then I would suggest an OS specifically designed as a VM environment (or hypervisor type setup) something such as Proxmox VE (my personal favourite) or VMware ESXi or similar.