Most of the stations in your stronghold come with Lost Ark Gold tiers which can be delocked by using your lab. If you see an option like "Manor Lv. 2" or "Workshop Lv. 2," make it a priority to investigate those. The research you do will open more possibilities in your stronghold and progress certain quest lines pertaining to the system. Some of the options will require your strength to be the desired level. If you're trying to upgrade an component of your strength but can't, you likely require upgrading your stronghold level.
Lost Ark Stonghold View Research Tip
You can see the requirements of each upgrade to a stronghold by clicking "All Research" from The drop-down menu at the top of the Lab UI. In the case of workshops, simply uncheck the "View Craftable" box to see every recipe.
As with your characters strongholds too have a level of their own. You earn stronghold XP by doing, yes, working with your stronghold. Crafting, researching, and dispatching crew members to Buy Lost Ark Power leveling missions all provide stronghold XP. The most effective way to upgrade your stronghold is to complete station-based missions, so be sure that your stronghold is always in operation whenever you're playing Lost Ark.