Lava deals an appropriate amount of damage for the level of the characters and the intensity of the challenge you want them to face.
4e doesn't use static numbers based on the objective source of the damage; in 4e the mechanics scale with the party, according to the thing's role in the story, in order to challenge the group appropriately.
Lava is probably a pretty intense challenge, so I'd use maximum damage values for the level of the challenge it's appearing in. To get a feeling for the right amount of damage I'd look at powerful hazards of the right challenge rating, and at daily powers of monsters in that same range (using MM3 and later monsters because monster design was re-tuned at that point in the edition's development cycle). I might also/instead use a table like Level 1 Equivalent damage; I've had great success with the damage values on that table for all my monster/world needs.
Then I'd have to figure out the lava's role in the scene: is it active or passive? An active lava hazard has its own initiative turn and deals damage on that turn. A passive lava hazard deals damage whenever a creature enters its area and at the start of each turn thereafter. Either way, the character's probably taking damage each turn he stays in the lava, and fire resistance applies to each instance of the damage. I wouldn't have an attack roll because he's wading through lava--the "attack" should land automatically. (If I were allowing an attack, miss would deal half damage and I'd dramatically increase the total damage the attack could deal.)
Lava's probably also going to count as difficult terrain, making it take longer for the character to wade through--probably increasing the number of turns he's spending taking damage.
What might this all look like? Here's my off-the-cuff "river of lava" hazard, with the level-dependent numbers scrubbed out.
River of Lava (level X obstacle)
A shallow river of lava oozes slowly.
Hazard: Lava fills each square of the riverbed, turning it into difficult terrain.
Perception: No check is required to notice the lava.
Trigger: Whenever a character enters the lava river or starts their turn in one of its squares, they take XdY+Z fire damage and are targeted by a Relentess Flow attack.
Attack: Relentless Flow
Opportunity Action (melee)
Target: triggering creature
Attack: +XX vs Fortitude
Hit: the target is slid 3 squares downriver.
Miss: the target is slid 1 square downriver.
This means that with high enough resistance a character could walk through my lava hazard undamaged, even if the cumulative damage the lava tries to deal him is much higher than his resistance. This is, I think, in keeping with the spirit of 4e: heroes are awesome beyond all reason.
The best relation is the Falling Roof Trap listed in the DMG and Phandelver Module. If triggered, it deals 4d10 bludgeoning damage, but allows for a DEX save. Here, you're dropping something significantly larger, from a greater height.
You can reach back further to 3.5 and compare it against the Siege Engines. A heavy Catapult launches a sizable stone for 6d6 bludgeoning after traveling an arc with a base of at least 100 ft. Again, this is something larger, falling from a greater height.
The math for this starts with the understanding the surface area of the impact to determine the DC for a dex save, a perception check with a decreasing DC to perceive the falling man, and an estimation of the mass of the falling object. For a base assumption, refer to page 249 of the DMG for Improvising Damage. This is less than a crashing flying fortress, but more than compacting walls. In terms of Damage Severity, this should be at least deadly for any one caught in the center of the target area, and dangerous for those on the edge.
Best Answer
Damage Bounds
On page 249 of the DMG, we have a section on Improvising Damage. On the chart are a few interesting things we can use to determine a damage amount.
For a lower bound we can use "stumbling into a fire pit" at 2d10. While yes, the creature didn't fall into the lava pool and only their feet are potentially directly exposed, lava is really hot (see below) and the proximity puts you at danger for second degree burns all over.
For our upper bound, we have a far more directly relevant 10d10 damage for "wading through lava". The creature isn't wading through lava here, they're walking across it, so it certainly wouldn't exceed 10d10.
My Ruling (feel free to disagree)
Depending on how active/fresh the lava is I would put it between 2d10 and 6d10 damage. I would default to the middle of that range at 4d10 but the choice is entirely the DM's.
Little bit of info about real-world lava and boots
Average liquification temperature of rocks is around 800-1200 degrees Celsius. Leather starts to burn around 200 degrees Celsius. Real life leather boots are going to melt really, really fast, even just being near the surface. Iron boots, with a melting point of 1538 degrees Celsius have a much better chance of survival, though they still are really good conductors of heat. The radiant heat is still going to hurt if they are even on the edge of the lava stream.
Additional clarification
Since people are questioning whether ring of water walking works on lava, it would entirely depend on if lava is liquid, see definition of the ring. OP appears to treat lava as liquid in their question, and the spell waterwalk "grants the ability to move across any liquid surface--such as water, acid, mud, snow, quicksand, or lava--as if it were harmless solid ground", so yes, in D&D 5e, lava is liquid, and per the Improvising Damage section (DMG249), you can wade through or be submerged in it, real world lava mechanics notwithstanding