These two games were my teenage years!

I wonder if there are games inspired by LoM and DR. Like Freeciv is of Civilization. I did try to look from web, but couldn't find.
Because, I think these games would deserve to be modernized.
Don't get me wrong: I love the originals. And so great that these games have been updated to newer versions!

Runestone and Sorderon's Shadow. But they are almost as old, and are more Adventure games than Strategy.
There's also a newer game that is more like LoM and DR, which I haven't played, called Legions of Ashworld, which is probably your best bet.

I'm always surprised more games didn't copy the turn based 3D element of these games.

I know of one new game (by me!) - Fernageddon.

For slightly newer games, check out Midwinter (also by Mike Singleton) fits. Through it is more action focused, but it's the same general idea of using your small initial team of people to find and recruit other people who you then control. All while the enemy side is using their army to take over the island.

It is heavily flawed, with it using a mouse control interface that's a bit laggy on the 3D sections, and - well - it is late 80s 3D... Also you can easily win by just storming the enemy's base at the start. But the concept is pretty cool and takes the good points of LoM.

It is a pity very few people took up this style of game, as it's an interesting way to do a war game.