However, there is a pull requests which fixes this, slated for release in v0.20.0 [1]. The pull requests is beneficial for CPFP as the node would be able to fetch the parent transaction after seeing the child transaction.
[1] https://github.com/bitcoin/bitcoin/pull/16851
Very cool... thank you. I had seen an article or interview with some LN people and they were discussing a proposal to handle cooperative closing with a form of CPFP. The idea was that either, or both operators could broadcast a 0 sat/b txn. This would give a little more options for handling the channel reserve and allow both parties to split the cost of closing with 0 sat/b + CPFP. Of course the same could be done for the opening channel TXN as well.