I am running FME Desktop 2020 and I am using the RealDWG AutoCAD Writer. One of the parameters in the writer (not sure if it was in previous versions) is AutoCAD Shape File Folder.
You can reference the system folder where the file is located (The file is provided with your copy of AutoCAD on your system) or you can copy it from your local machine to a network folder somewhere and reference that folder.
The ltypeshp.shx file is provided by Autodesk with your version of AutoCAD at the following location on your system.
C:\\Program Files\\Autodesk\\AutoCAD 20xx\\UserDataCache\\Support
Look for ltypeshp.shx. If you still cannot find it, go to your C drive, select program files, and go into the Autodesk folder. From there use the search function to look in the folder for .shx. When it comes up with the list, find the file, select it, right-click, and choose "Open Folder Location". You can then copy that file from its location to wherever you need it to go.
I spent a lot of time looking this up and found pieces of it in a couple different forum posts and ultimately this completely got rid of the warning.