> As the access to Lightning is also by the (same?) ASP, it seems to me that 
> the ASP will simply fail to forward the payment on the broader Lightning 
> network after it has replaced the in-mempool transaction, preventing 
> recipients from actually being able to rely on any received funds existing 
> until the next pool transaction is confirmed.

Yes, that's correct. Lightning payments are routed through ASPs. ASP may not 
cooperate in forwarding HTLC(s) AFTER double-spending their pool transaction. 
However, it's a footgun if ASP forwards HTLC(s) BEFORE double-spending their 
pool transaction. 

What makes Ark magical is, in the collaborative case, users' ability to pay 
lightning invoices with their zero-conf vTXOs, without waiting for on-chain 
confirmations. 

This is the opposite of swap-ins, where users SHOULD wait for on-chain 
confirmations before revealing their preimage of the HODL invoice; otherwise, 
the swap service provider can steal users' sats by double-spending their 
zero-conf HTLC.
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