1 - When you dig veins, as much as possible don't do it from your base, but from the exterior toward your base. This way you'll greatly minimize the odds to open a new pathway toward your base, which is probably the worst possible outcome ever in a tower defense game like Lumencraft.
Said differently, so that it is clearly understood AND applied: starting from your base and digging tunnels might mean you suddenly open up a new cavern/area which is connected to the rest of the map and the invasion waves. You just raised the difficulty level by one doing so.

2 - The maps often gates juicy veins behind hard rocks, thus preventing you to access them until you upgrade your drill. And upgrading requires a lot of Lumen. Eventually (well asap,) you'll upgrade it, but what can you do before this time? There is a solution requiring only base metal: dynamite from the explosion workshop! Use it profusely, as the 20 metals you pay will be largely compensated by the amount of stuff you can mine instantly with it.
The dynamite does not harm you.
The dynamite, once dropped, can be further pushed slightly toward the wall by moving onto it.
It can damages monsters if you have nothing else.

3 - Some maps feature little crevasses in the ground, which indicates a minor spider nest.

4 - You can recycle everything, including items and ammo.

5 - Power relays and containers can be placed even outside the power grid if they are covered by another power relay yet-to-be-constructed. Rinse & Repeat.

6 - Construction Drones originate from the nearest Container, and not only from the Reactor.

7 - Repair gun can also work as a tractor beam, grabbing anything and carrying it. You only spend one charge if you maintain the mouse button. This includes the explosive barrels (very practical to place them), and already laid mines, you want to reposition. In case of need, you can also transport one extra item, if you are short on inventory space. Special hint: In Fear the Darkness, you can transport Golden Lumen crystal with it.

8 - Arthroma can be used to dig for you. As you may have noticed, they pause a bit before charging straight, like a bull. Doing so, they can dig into anything like a level 5 drill. With some side-stepping, you can definitely entice an Arthroma to pierce this metal complex you want to explore.

More tricks are incoming if they are worth my time, and yours.