I'm looking for a dock supporting not only launchers but also a list of currently running apps that is fairly lightweight and suited for Lubuntu install.
Docky is a great dock which if used in combination with the the light-weight compositor xcompmgr provides a simple customisable dock. It does install the mono-libraries but I havent noticed any sizable increase in resource usage.
Some simple docklets come as standard e.g. clipper and clock as shown. For other applications, you can pin them to the dock to launch them.
More customisable but needs effort to start with is Cairo-dock. Out of the box, it assumes you have various default gnome applications. You will need to either remove these or edit the applet to launch the Lubuntu equivalent. But, personnally, I think the small amount of effort is greatly outweighed by the great 3D effects - use it with the light-weight compositor xcompmgr.
AWN was always a favourite of mine under Gnome - however avoid this one for Lubuntu because Synaptic tries to install most of the Gnome desktop when installing AWN.
However, if AWN is installed from the command line using the command "sudo apt-get install avant-window-navigator --no-install-recommends" it doesn't install all the Gnome packages, but it will take some manual tweaking after install as you'll need to install the packages for whatever applets you want one-by-one. Doing it this way does give you AWN with a very light install size.
WBar - various people have raved about this. Personally, don't know why - it really is just a very light-weight launcher. No additional applets come with it. All of the configuration you have to do via manually modifying a text configuration file.
Wbar is lightweight and won't install unwanted dependencies. It's quite customizable yet simple.
Use lxpanel to make a dock - http://lubuntu.net/blog/lubuntu-screencast-lxpanel-2-panel-layout