SAO and LH are not based on any existing MMO. Depending on which MMORPG's you have played you will likely find certain aspects of the world to be incredibly consistent with it.
The grand-daddy of all MMORPG's as they play right now is Ultima Online (which I played during beta) as the crafting and "loss of experience upon death" both originated here, and it even predates EverQuest, as you could craft in previous Ultima games since at least Ultima 4 (magic spells), 6 and 7 (food). Likewise, player-owned housing originates in Ultima Online.
As far as Asian MMORPG's influence, LH's world is a bit more consistent with Final Fantasy XIV (and likely XI), while SAO is very consistent with Mabinogi. In game, marriage is something that was introduced in a Nexon game that predates Mabinogi (called NexusTK:Kingdom of the Winds, which is a game I also played during beta).
Dungeon Raids, as they are in SAO and LH, are shown as a type of instancing system which is fairly consistent with the advent of 3D modern MMORPG's, though based on the explicit references to roles (eg Tank) and menu driven combat with cooldown's, this might have its origins in EverQuest, but this is fairly consistent with FFXI/FFXIV at present.
The respawn rules, how monsters respawn in the same area, which is something that both Ultima Online and NexusTK did in 1998.
Guilds is a strange aspect. The original 2D MMORPG's never had guilds (it may have originated in Lineage) and it was just something people started doing, so later games actually introduced it as a game mechanic (and indeed the entire point of Guild Wars). Likewise, the PK elements were also something that existed originally in UO, but EverQuest was probably the first to see abuse of it, as in SAO.
Take for example the pets and mounts. In LH the pet griffon mount is also a flying mount that is available in Mabonogi. Likewise in SAO, Silica has a combat pet. Combat pets have been in MMORPG's for quite a while. However, virtual pets actually originated with Tamagotchi's, which actually die if you don't take care of them. So again depending on your point of view.
As for the races and classes, SAO was primarily humans, while SAO:Alfhiem is actually based on Lore from "A Midsummer Night's Dream" which is Shakespeare. The races in LH are the standard human-like characters from Tolkien (LOTR) with the were-animal races (which the current game out there that has these is TERA).
And to round this out, the "Fighter, Wizard, Thief, Cleric" type of roles originate in tabletop D&D games, but the way they are used (Tank, DPS, Healer) originates in Wizardry, which was more popular in Japan than it was in the West. Permadeath (SAO) also originates in Wizardry.
In respect to LH, since there is a specific reference to 1998.10.22 and the character in episode 14 specifically mentions 8 levels of magic which is also something that Ultima has. Like if you want to use the date as a piece of proof, that means the game in question would have been in open beta on or after 1998.10.22, which chronologically can only be EverQuest. I've personally played the EverQuest Beta in 1998.
In one of the most recent episodes of LH (you need to pay close attention) you'll also realize that they are partied with an NPC. Most MMORPG's don't let you adhoc have any NPC join, they either are temporary for a quest (escort missions), or summonable partners/pets.
So as you see, it depends on which games you've played. When I talked to friends about SAO, they can find individual aspects of it that they related to their MMORPG of choice. Over time (at least since WoW) most games have borrowed ideas from each other enough that they're all becoming exactly the same game. They're only differing by environment (Fantasy like SAO), race/monster names (many are derived from Tolkien/D&D) and cost to play.
So there is no one right answer, as no single game introduced everything seen in SAO and LH at launch. You can read comics/manga like 1/2 Prince or Yureka that also deal with virtual worlds and you'll see much of the same elements there as well.
The interesting moral question that comes up again in all of these stories based on MMORPG's is "are we losing our humanity" by when we treat AI's as tools.