Ashnod's Coupon has the ability:

{T}, Sacrifice Ashnod’s Coupon: Target player gets you target drink.

Errata: You pay any costs for the drink.

Meanwhile, R&D's Secret Lair says:

Play cards as written. Ignore all errata.

Ignoring the fact that R&D's Secret Lair now has errata to make its mana producing ability still work (which is baffling to think through), how does R&D's Secret Lair interact with Ashnod's Coupon? The issue with Ashnod's Coupon is that the Coupon's errata is printed on the card. Thus, it is errata (so you should ignore it) but is also part of the card as written (so you should use it). Which one happens?

While R&D's Secret Lair is on the battlefield, you should not ignore the "errata" printed on Ashnod's Coupon. The Coupon's controller still pays any costs for the drink. Mark Rosewater, the official silver-bordered rules manager, published the following ruling:

kingdavidofisrael asked: Does R&D's Secret Lair remove the errata from Ashnod's Coupon, or will I still have to pay for the drink?

R&D Secret Lair contradicts itself as it asks you to play “all cards as written” and “ignore all errata”. Ashnod’s coupons errata is written on the card.

This means I can basically rule either way so I have opted to rule in favor against dumb shenanigans. (Note I’m all for regular shenanigans when playing with Un-cards.) Owner of the Ashnod’s Coupon pays for the drink.

The first linked article, authored by Mark Rosewater and published on the Wizards of the Coast official website contains the following statements:

I wear many hats at Wizards of the Coast, one of which is that of silver-bordered rules manager.

Most of the time, being silver-bordered rules manager is easy—I just get the occasional question on Twitter or my blog.

If you have a question I didn't address, you can write to me at my blog for an answer.

Therefore, Mark Rosewater's role as silver-bordered rules manager is officially sanctioned by Wizards of the Coast, and when he answers ruling questions about silver-bordered cards he is doing so in his official capacity as silver-bordered rules manager. So, his rulings on his blog have the same force of authority that the main rules manager's rulings have on the main game.

In typical silver-border fashion, things have gotten a bit contradictory...

A more recent post by Silver-border Rules Manager Mark Rosewater, has ruled in the opposite direction to the other answers (that refer to an earlier ruling):

nicthos asked: Un-question: if you use ashnod's coupon and you have R&D's secret lab out, who pays for the drink?

MaRo: They do. Note that they can concede in response to the activation.
March 10, 2019

So who pays?

As Un-sets are silver-bordered, they are by definition for casual play. So talk with your play group and agree on how you wish to rule this interaction so that it is enjoyable for those in the group. Allow everyone to make their arguments beforehand so that when it comes up in-game everyone is familiar with the interaction and can quickly move on with the game.

^{Side Note: I suspect that someone will point out this contradiction to MaRo sometime in the future, so expect this answer to be changed again sometime soon.}

This can go either way. Silver bordered card rulings are complicated (see the caveats below) and Mark Rosewater has issued conflicting rulings on this.

Mark Rosewater's Rulings

MaRo's original ruling on the subject is that the owner of Ashnod's Coupon still pays for the drink:

R&D Secret Lair contradicts itself as it asks you to play “all cards as written” and “ignore all errata”. Ashnod’s coupons errata is written on the card.

This means I can basically rule either way so I have opted to rule in favor against dumb shenanigans. (Note I’m all for regular shenanigans when playing with Un-cards.) Owner of the Ashnod’s Coupon pays for the drink.

MaRo's later ruling on the subject (thank you @Malco for finding this) is that the other player pays for the drink:

If you use ashnod's coupon and you have R&D's secret lab out, who pays for the drink?

They do. Note that they can concede in response to the activation.

Silver Bordered Card Rulings

Silver bordered cards are complicated. The official magic rules say the following:

Silver-Bordered

Cards in certain sets and certain promotional cards are printed with a silver border. Silver-bordered cards are intended for casual play and may have features and text that aren't covered by these rules.

Wizards does not publish official rulings on silver bordered cards the same way they do on regular cards. Mark Rosewater (MaRo) is Magic's "Silver Bordered Rules Manager" as mentioned in the FAQs for Unhinged and Unstable, the later of which lists MaRo's blog as a resource for answers to additional questions on silver bordered sets. While these are official publications of Wizards, they are not included in the regular rules cannon, and so absolutely do not have the same force of authority as the main magic rules or card rulings.

MaRo has said:

One of the wonderful things about silver-bordered cards is that we can do stuff that maybe doesn't technically work but that players would have lots of fun trying to make work.

Silver bordered cards were never intended to have a coherent rules framework. This is visible in MaRo's own discussion of this situation, where he describes the iteration between these two cards as "contradictory" given the magic rules framework, and his ruling was based on a personal philosophy rather than any logic of the rules.

My Personal Opinion

I believe that the targeted player pays for the drink.

Even in MaRo's original ruling, he claimed that the interaction could go either way. "Ignore all Errata" is its own sentence, and thus can function as an independent part of the ability: first, play all cards as written, and second, ignore all errata. Under this interpretation, the errata on Ashnod's Coupon is nullified by R&D's Secret Lair, and the target player will have to pay for the drink.

In this case (as highlighted by MaRo's later ruling), a player can still conceded the game at any time. Thus, this combo, targeting a sufficiently expensive drink (such as a bottle of 50-year Macallan, retail price $30,000), effectively becomes "Target player loses the game". This makes it a 2-card 0-mana win combo, which is the simplest first turn win combo in all of magic. The downside (?) to this combo is that a player does have the option to buy you a $30,000 bottle of scotch to prevent themselves from losing.