I think we might be having a terminology / nomenclature problem. You keep using the word 'pierce'. Usually when a tool pierces something, we think of a needle going through that thin piece of silicone used to prevent babies. No metal working tool ever pierces material in this way. Even if you have the hardest possible tool, and the softest possible metal (or even wood), you can't pierce the material. Maybe if you used the tool in a shotgun you could get enough energy, but that's not any kind of controlled or precision way.
Instead, metal working tools 'scrape' small amounts of material from the surface. On some machines, the tool moves over the work, on others the tool is stationary and the work moves. On a lathe, both the tool and work move. The work rotates, and the tool moves left and right and in and out (yes, I'm skipping details). The 'scraping' happens where the edge of the tool contacts the surface of the rotating work. How much material you are trying to scrape off in a single pass is given by your depth of cut (how far towards the center the tip of your tool extends into the work) and you feed rate (how far to the left or right the tip of your tool has moved since the last time this point on the work was at the tool).
If you have ever scraped ice off of a side walk, you know that only the very edge of your tool actually works the ice. And there is a huge difference in the effectiveness depending on how you hold the shovel / ice scraper etc. Ice is very much softer and more brittle than whatever your shovel is made of, and as a human you can provide only a very small amount of power. The best results come from a very steep rake angle. On the lathe, the situation is different. The difference in material between what you are trying to scrape and what you are scraping with is much less, and the power available is much greater. This leads to good results coming from a very shallow rake angle - you shouldn't, but you can even use the square chunk of HSS directly without grinding any angle into it.
You don't want to do that for a couple of reasons. The most important one being clearance - if you scrape ice of the sidewalk, you don't want the whole rest of the shovel to scrape on the pavement too. That just makes the job harder and grinds down your shovel.
And you do want some rake angle. How much? That depends on many factors, but for steel on HSS it's not zero. Some materials you want a negative rake (think plastic), but not for steel or any metal you are ever likely to see. There are lots of tables that you could consult, but the key factors are how high your tool is with respect to the centerline of the work, and at what angle the tool itself is being held. Modern tool posts try to make this easier by eliminating the second parameter, but thew older 'rocker' style tool posts allow a great degree of flexibility. You want to have the tip of the tool engage the work slightly below the center line (so that it will bend up and away if there is a problem) and at an angle something like 10-15 degrees as a rule of thumb. That number is a total guess and your milage will vary. In general, the rake angle is the most important, and relief angles just have to be large enough to provide adequate relief (the bottom of the tool clears the work) without undermining the cutting edge (anything less than 45 degrees should be safe)
Inserts have complex geometry with curves and other specialized features. Even a short discussion of those would take a book