Reduce the number of data sources
Sounds dumb right? Well, it's not totally true. Of course, for native Google or third-party connectors, there is no way to overcome having various data sources. But for database connections, you might be able to combine them so instead of having 3 different data sources to get 3 metrics, try to mix them into one. It's all about calculation efficiency here, and believe me, it works.
Use views instead of queries for databases data sources
Linked to the previous one, what about relocating the calculation outside of Looker Studio? Indeed, when you're using a query, you're asking Looker Studio to pull loads of data and make a lots of transformation. It's way more efficient to give it a cached table ready to be read by using views.
Change data freshness frequency
For viewers, Looker Studio relies on cached data (for editors, I believe data gets updated every time you open the dashboard, so not much you can do here). So try not to refresh data too often, select the longest delay data freshness (usually 12 hours), for most reports people don't need last minute data. You can find this option under Resource, Manage added data sources, Edit, and then top right of your screen, Data freshness: