I'd lean toward saying you're expecting too much of a new player unless you do a superb job teaching the player strategy in your game.
A lot of games reward taking on lots of encounters throughout a dungeon and in certain games (ones with a high EXP curve and easy battles), it's the only way to be at a high enough level to take down the dungeon's boss. So you need to clearly get the point across that they shouldn't be "ramboing", or you're going to turn off half your players immediately. Okay, that's not so hard to get across. You could have the main character's mentor, or one of the party members, say so outright.
But then battle strategy isn't quite as easy to teach. An experienced RPG gamer might be able to figure out the "approprite times" to use each skill but you can't count on every new player knowing this from the outset. Same with knowing to take out the two skeletons before the lich (a classic RPG Troop strategy, but not something you find a lot of outside RPGs). And game overs via pure luck (even extreme unluckiness) is absolutely something to avoid in general, especially in the very early game.
Try to come up with any "halfway reasonable" strategy that players might take on as they play your first dungeon, playtest, and see whether you're able to pull out a victory. If not, make the level forgiving enough that even these suboptimal strategies grant a victory every time. Maybe have one somewhat "overpowered", temporary character that can demolish all of the enemies by themselves even if the rest of your party falls (letting the player know they're doing something wrong without forcing a Game Over). Reduce the boss' HP by 10 or 20 percent. Script it to deal less damage if the party is in trouble. Consider decreasing the damage that skeletons do (and immediately destroying them if the Lich is defeated) so that you're not penalizing players that go right for the Lich. And figure out ways to reduce the luck factor on that boss. Maybe he doesn't use the nuke if you're below half health, or if he has already used it twice.
Basically, your player will usually need some time to learn the mechanics of your game and figure out how to respond to them. Unless the game's core engagement is challenge (in the sense of overcoming obstacles that present a real chance of failure), a Game Over in the first dungeon (short of incredibly dumb play) is strictly bad design. A Game Over in the second dungeon is likely to frustrate the player and ****** their ability to develop a flow state when playing your game. The third dungeon seems to me like a good time to give below-average players a wake-up call with a very real possibility of GO's, now that they understand how the game works and have gotten into its flow.
Could the player figure all this out within a few runs, after their initial attempts at ramboing, then going straight for the Lich, fail? Eh, probably. Will they stick around long enough to do so after they fail a couple times, using strategies that may have worked in other games they've played? I worry that they won't stick around, unless your game is unbelievably fun or compelling. That's why I really recommend erring on the side of generosity early on, and doubly so if you're not guiding the player along with heavy instruction.