The converter tool you modified
When you downloaded the tool it was under LGPL. So, normally you should have published your modifications under that license. But you say that it is now available under Apache 2.0. Are all versions of the tool now also licensed under this new license or is it just new versions? If it's just new versions, you should make sure that your modifications apply to a version whose code is currently released under Apache 2.0 before publishing your modified version under this license as well. Otherwise, you could have published them under the original LGPL license.
You should also quickly check that the license change seems legitimate. Typically, if the converter tool was the work of one single author, then it's probably legitimate. In other cases, that can be more complicated.
The converter tool you created
You can publish this one under any license you wish as it is your own work.
The combination of the two converter tools
This "whole work" can only be published under a license which its dependencies are compatible with. Whether the converter tool you modified should have been licensed under Apache or LGPL does not change much to the game because both of these licenses are compatible with AGPL 3.0 and GPL 3.0. So feel free to use one of these for the whole work.