The best free alternative to Lucidchart is diagrams.net, which is both free and Open Source. If that doesn't suit you, our users have ranked more than 100 alternatives to Lucidchart and loads of them is free so hopefully you can find a suitable replacement. Other interesting free alternatives to Lucidchart are Dia (Free, Open Source), yEd Graph Editor (Free), LibreOffice - Draw (Free, Open Source) and Freeplane (Free, Open Source).
Minzel is a beautiful and free mindmapping tool built for creatives and gives you the power to visualize your thoughts. It is simple to use and allows fast and productive mind mapping. You can use Minzel on every modern browser.
Umbrello is a Unified Modelling Language (UML) modelling tool and code generator. It can create diagrams of software and other systems in the industry-standard UML format, and can also generate code from UML diagrams in a variety of programming languages.
Heimer is a desktop application for creating mind maps and other suitable diagrams. It's written in Qt and targeted for Linux and Windows. Features: Easy-to-use UI Very fast Zoom in/out/fit Zoom with mouse wheel Save/load in XML-based .
The PlantText tool is an online tool for quickly creating UML (Unified Modeling Language) diagrams. Unlike most tools, PlantText can build diagrams without the use of a mouse because it is based on PlantUML markup language.