After playing Larn for many years, and over much trial and error, I've developed what I call the "Volcano Lottery" strategy. Using this strategy got me quickly from difficult 4 to difficulty 9. (in the UNIX version of the game that I play, beating difficult 8 doesn't automatically increase the difficulty to 9 for some reason, but you can still play that difficulty by manually entering it at the start by typing Larn -9 at the UNIX prompt).
I start off using some of the same strategies as I mentioned earlier--saving all scrolls and drinking all potions. I sneak around level 1 until I have enough gold to buy chain-mail and a flail. The weapon is entirely optional, but typically the 1745 I get from selling a chest to the trading post is the source of my initial funds. The armor is the most important of the two obviously. Once I have that armor, I complete the first two levels. I sell all gems and all rings/equipment/books. If I'm feeling lucky I might try to pry a throne or two as well. The goal is to get 13,100gp in the bank. This will allow you to purchase a Stealth scroll (3000gp) a Magic Mapping scroll (4000gp) and a Pulverization scroll (6100gp). With this combination you then dump any excess equipment to get your weight down (to keep from falling down the volcano shaft) and read the stealth scroll. Then you climb down into the volcano. As long as you haven't recently read an aggravate monsters scroll you will be able to sneak around the Volcano without monsters getting you. If you think that the monsters may be aggravated, go to the college of larn and take a 10 mobul course, such as Contemporary Dance so it wears off. Also be sure to deposit any excess gold in the bank. It will weight you down and in the bank it earns interest (more on that later).
Once you are inside the Volcano with Stealth active, read your magic mapping scroll. Scan the level for Books and Chests. Books from level one of the volcano are worth 25,418gp in the trading post. Chests are worth 56,988 gp! Just one chest or a couple books can set you up at the beginning of the game! If you get a chest and 2 or 3 books, you can deposit the gold in the bank except for 2000gp, then take all the courses in the college of larn. You will have enough money to buy the Lance of Death at this point because of the accumulated interest.
The pulverization scroll is important to this because since you can't hit or kill the monsters, you have to be able to get a path TO the books or chests in the volcano. This will sometimes include knocking down a wall. If you want, you can try to use the Pulverization to kill a high-level monster such as a Naga (n) or a Purple Worm (P) or any non-green Dragon. That will raise you automatically to 10th level. Once you reach 10th level you can hit Shift-Z to teleport! Then you can teleport around the volcano collecting books and chests. You just have to make sure that you don't hit a monster and lose your stealth, open a door that acts as an aggravate monster scroll, or fall into a bottomless pit on V3. Chests from the third level of the volcano sell for over 100,000gp. It's not very hard to come out of the volcano with a couple chests and two or three books and have enough money for the Lance of Death, Stainless Steel Plate armor, all the rings/scrolls/potions you want. Then you can cruise down to 10th level of the dungeons with very little problems. I always go down to the 10th and kill the demon guarding the Eye of Larn (even if I don't take the Eye) because the journey down there will increase your level and you'll find lots of other buffs on the way (spells, enchant weapon scrolls, enchant armor scrolls, etc). It's also nice not to need money on the way down to the 10th level since you don't then have to lug around all the gems you find.
Volcano Lottery has worked for me almost every time. At the very least there's usually a chest or a couple books you can grab from level one. Even if you can't afford the lance of death right off, you can usually get all the armor you need and a "gem perfection" scroll. Then you can stockpile your gems until you find another gem perfection scroll. Even books from the lower levels of the dungeons are worth a decent amount of money. As long as you have a good offensive spell (fireball or lightning or dehydration) you're not missing much by selling the books if you need to in order to get the lance of death.
There have been times when I've gotten enough money or the stealth/mapping/pulverization combo before even completing the first level of the dungeon and I've ended up with 250,000-300,000 gp from books and chests from the volcano. If you happen to find an annihilation scroll before heading down, you can read it next to a group of Dragons or something and jump your player level up pretty far.
When you do get back down to V3 to defeat the last demon and get the potion of cure dianthorritis, I've found that it's easiest to keep a scroll of hold monster handy to freeze the demon. Then you can try to hit it. Only one hit will kill it, but they're hard to hit. Stealth works as well, you just have to hit it before either of them runs out.
A couple more things to note: Coming out of the volcano, you have to be as unencumbered as possible before trying to get out of there with one or two chests and a couple books. I usually have to dump my armor and all my gold in order to get up the shaft. It's more than worth it, of coruse.
Another fun easter egg I found, was that if you have 500,000gp in the bank of larn you get a popup that by law only deposits less than 500,000gp can earn interest. That cracked me up.