The default executable file format in Lubuntu is a DEB file. Compare to RPM in some other Linux distributions, DMG in Mac OS, or MSI (or EXE) in Windows.
See InstallingSoftware on the Ubuntu Community Help Wiki.
The quickest way to download, update, upgrade, install and remove software is via the command-line with APT (Advanced Packaging Tool).
Go to Menu --> Accessories --> LXTerminal (or Ctrl+Alt+T)
Update the list of software available,
type: sudo apt update
Install a software package,
type: sudo apt install name-of-the-package
Upgrade all (upgradable) installed software,
type: sudo apt upgrade
Upgrade the Operating System,
type: sudo apt full-upgrade
Remove a software package,
type: sudo apt remove name-of-the-package
Purge a software package, it’s dependencies and it’s configuration files,
type: sudo apt purge name-of-the-package
Automatically remove all unneeded dependencies,
type: sudo apt autoremove name-of-the-package
Apt-url allows software packages to be installed by a click of a button (a special link) on a webpage viewed with a web browser like Firefox.
The Apt-url protocol is a mini-application for installing packages from a repository the user already has enabled.
MORE INFO: See also AptURL on the Ubuntu Community Help Wiki.
When downloading a .deb file, you'll have the option to open (and install) with GDebi. If you've already downloaded a .deb file; just double-click it to automatically use GDebi. Alternatively, go to Menu --> System Tools --> GDebi Package Installer and browse to find an already downloaded software package (or, one in a removable medium) to install.
See Using GDebi to Install Packages on the Ubuntu Community Help Wiki.
The Lubuntu Software Center will show you several hand-picked packages for Lubuntu. Go to Menu --> System Tools --> Lubuntu Software Center Browse through a small collection of featured applications, categories and single packages. Search, read descriptions and add the packages you like to the "Apps Basket." This acts as a shopping cart feature. When your done browsing; click the Apps Basket button, review your choices and install.
See Lubuntu Software Center in Launchpad. Also see the web version of the Ubuntu Software Center.
Snap is a new package format that contain all the dependencies needed to run instead of relying on shared libraries. Snaps are planned to be Linux ubiquitous; already working on every *buntu derivitive (U/X/K/Lubuntu), as well as Arch, Debian, Fedora and more. Snaps are designed to work as well on the cloud, servers,phones and other devices as they do on the various Linux distros they’re supported on.
See Snap Packages on ubuntu.com, Universal “snap” packages launch on multiple Linux distros on Ubuntu Insights, How to Install and Manage Snap Packages on Ubuntu 16.04 LTS on HowToGeek, and Using Snap Packages In Ubuntu [Complete Beginners Guide] on It’s FOSS.
Browse through almost 30,000 available packages with Synaptic Package Manager. Go to Menu --> System Tools --> Synaptic Package Manager. Read the descriptions and mark the check boxes of ones you want with a click of the mouse. When you're ready to install, click the "Apply" check mark. You can also remove and reinstall and / or fix broken packages.