Firstly, in the wiki page Handoko mentions it says -
On a DEB based system, you almost certainly should use gdebi to install any downloaded DEB.
Please don't use the Ubuntu Software Install tool with downloaded debs. There are reports of the 16.04 version making a number of 'mistakes' installing downloaded debs and the 1.8.4 one still has some issues.
Your issue with reports about 1.8.4 makes sense if you have had 1.8.4 running in the past. On any (recent) version of Lazarus, the config ends up in $HOME/.lazarus So, when you bring up a different version it will find it. And generally offer to update it, reasonable thing to do.
Not having menu and icons installed for Lazarus is more interesting. Looks like the deb puts an icon in /usr/share/pixmaps/lazarus.png - is that present ? For it to be used, the desktop file must exist - /usr/share/applications/lazarus.desktop - is that present ?
Are you are expecting to be able to double click on a .lpr file and have the OS load up Lazarus for you ? Not sure it will. Cannot test as I don't install Lazarus from Debs. Anyone ?
Honestly, assuming you still have the install debs handy, first thing I would do is use synaptic to remove the all three, use synaptic to install gdebi (if you don't have it already) and then use gdebi to reinstall those debs. Clean out $HOME/.lazarus first if you want to.
Davo