Hey! Before i can truly help you out i need you to do everything here step by step even if you've previously done so. Although im not 100% sure this will fix it.
Step 1: Navigate to Steam/SteamApps/Common/GarrysMod/garrysmod/addons
Step 2: Select ALL files within this folder and press "DELETE"
Step 3: Navigate to Steam/SteamApps/Common/GarrysMod/garrysmod/cache/workshop
Step 4: Select ALL .gma files (leave the resources folder) and press "DELETE"
Step 5: Navigate to Steam/SteamApps/Common/GarrysMod/garrysmod/cache/lua
Step 6: Select ALL files within this folder and press "DELETE"
Step 7: Navigate to Steam/SteamApps/Common/GarrysMod/garrysmod/download
Step 8: You guessed it, select ALL files within and press "DELETE"
Step 9: One last time, navigate to Steam/SteamApps/Common/GarrysMod/garrysmod/downloadlist
Step 10: Select ALL files within and press "DELETE"
First do key_listboundkeys in console and copy ALL of your binds or else youll lose all of them. Then close GMod
Save all the dupes in your dupe folder elsewhere or you WILL lose them all.
Make sure your launch options are empty. Steam > Right click on GMod > Properties and under General launch options should be empty.
In the Launch options box add +tv_nochat 1 and exit out of it.
Right click on GMod > Properties > Local Files > Browse > garrysmod > cache > delete the lua folder
Right click on GMod > Properties > Local Files > Browse > double click on FactoryReset-GMod.bat
Type Y and enter. When prompted again hit enter. The command box should close.
Let GMod validate all its files. Once it's done Launch the game
Load into Synergy, Watch the files it should stop on a file towards the end with a bunch of numbers and letters saying something like data/lua/numbers and letters
It may or may not retrieve 3000 LUA files from the server, give it a minute if it does it should install them quickly.
If it worked, look at your copied binds list and rebind your keys/put your dupes back into the advdupe2 folder. Be sure to remove the launch option when done
Generally this is to fix a Glua load issue but can also force certain things in your Garry's Mod to be reset and sometimes fixes issues related to downloading content via load in.