Imaro
Legend
Some of the mechanics are going to affect how dynamic a combat can be, even if it's less than the value of terrain. 3E was actually the worst for it, because it generally assumed miniatures and there were advantages to getting into a particular position and staying there (flanking and attacks of opportunity). 4E also generally assumed miniatures, but the mechanics generated a more dynamic combat (due to various forced movement and several movement powers). AD&D could be better for dynamic combat, depending on if you used miniatures or Theater of the Mind, because Theater of the Mind allowed for the most dynamic combats of all. 5E fits somewhere in the middle of all that, since positioning still matters even in TotM, but lacks 4E's constant movement that generated very dynamic combats.
Good use of terrain can make even a 3E combat fairly dynamic, but you should always consider the cost/benefit ratio. If it takes you a long time to make dynamic fights with terrain (which was often true in 3E), you should probably limit it to important combats. Adding one or two terrain features should take almost no time at all, but add some flavor to the combat, even if it doesn't make it very dynamic. Otherwise the combat sucks, as a DM of mine found out when every combat he ran was on a featureless grid (because he didn't think terrain should matter). Something else that can affect this is running a per-published adventure, as the OP is doing with RotRL, where combat locations are often already made (and designed for the style of the original edition).
I don't really want to get into a back and forth over editions so I'll just say that I also saw many fights in 4e, especially at the lower levels, degrade into fairly static battles because the terrain itself didn't reward forced movement (I mean you can push/pull/slide/etc. just because but IMO that's not really a dynamic combat). I think there has to be an incentive to use actions that promote dynamism in any edition or it's going to bog down to standard hit and damage tactics. Is it easier to prompt this type of combat in 4e rather than 3e...I'd sat probably yes (thought I'd argue 5e does a pretty good job of incorporating non-static features/spells into it's game as well) due to the various push/pull/shove powers but there still has to be a reason to use them (as opposed to say a power with bigger damage numbers) and that reason is usually terrain. I feel the same way about 5e's movement rules, some of it's Battlemaster maneuvers, Cunning Action, etc... if you give incentive players are going to utilize the fact that they can move, hide, move others, dash, etc. before or after attacks however if you don't they are going to go with hit and damage tactics because there's no reason not to.