Some more thoughts, as I work on other builds for this:
1) I imagine we would not want to call them Jedi in a D&D game, although its up to the DM as usual. For the nonce, I'm going to title them in honor of the registered user who started this thread: the Miklongi.
2) For a bit, I was also thinking of renaming the Force, but since force is one of the lightsaber's damage types, I realized that was pretty dumb.
3) Mr. Long did not include one legendary aspect of lightsabers, and I assume it was partly for this reason: putting a weapon equivalent to a vorpal sword in its ability to lop off body parts into the hands of a 1st level apprentice is kind of overpowered. Assuming vorpal swords do become available in future 5e supplements, it seems to me that until then it should not be added to the weapon's description. If vorpal weapons do join 5e, perhaps only the final lightsaber feat (master-level) would be capable of that feature.
4) The dark side. Are they out there? Does it seem reasonable to think they would be? I would think so. But I don't want to go there. It scares me.
5) Eldritch Knight, if a Jedi were to choose that Martial Archetype. The description in the PHB assigns the type of spells to the wizard class. Basing the linked spell-type on the sorcerer or warlock classes seems closer to the essence of the Jedi. I would just make that the player's choice. If someone does decide to make a dark-sider, aside from lightsaber damage, I think any damaging Eldritch Knight spells would deliver its damage by combining the force and shadow types (see Tormyr's reply re splitting damage dice above).
Well, that's it for now. Ciao!
Here are some of my thoughts on this.
1. I imagined this being a drop in replacement for Star Wars D20. Have spells be The Force. Martial weapons and heavy armor has a cortosis weave. The simple reskinning would potentially work in an era with a lot of force users, or a way to make the PCs special. Replace crossbows with blasters, etc.
2. If spells are the force, you can just reskin magic as the force. Just drop all material components that don't have a cost (the materials with a cost become components to focus on or transmute with the force.
3. In the old Star Wars card game from decipher, there was a card that let non jedi use a lightsaber, but it was dangerous to them. They had the ability to injure themselves. You could add a critical fumble for those not proficient in lightsabers. Since dropping someone to 0hp is the "killing blow," you could add a decapitation at 0 hp, but that might make the game less family friendly.
4. I imagine the Necromancy or the Death domain in the DMG would blend well with the dark side, or any of the evil alignments would provide a jedi with dark side leanings.
5. The eldritch knight is a great concept for an all around jedi. But lots of others would work as well. I think that most force abilities outside of spellcasting would work through feats (proficiency in an additional skills or tools through the force). A force sensitive rogue could learn how to use the force to aid intuition in use of thieves tools to gain expertise on its proficiency, etc.)
While this reskin with minimal conversion would be easier, it would tweak some of the flavor of the Star Wars universe. There is arguably more use of the force. Deities are dropped. Monks, Druids, Paladins, Eldritch Knights, Wizards, Sorcerers, Clerics, Arcane Tricksters and Rangers are all force sensitive/force trained/Jedi/Sith to some extent or another. Warlocks gain their force sensitivity from a gift from a dark benefactor? If everyone is willing to not be sticklers for "how things should be" in the star wars universe, it could be a relatively simple conversion.
My 7 year old daughter would love this. After starting her on First Fable, she liked it, but after haveing watched the entire Clone Wars cartoon, she told me in no uncertain terms that she wanted to be a Jedi. I could see picking up a Star Wars RPG adventure and having a relatively straightforward conversion to 5e without having to buy the Star Wars RPG source books.