The quick answer is, that there is no way in doing so, but let us imagine the workflow from a theoretical standpoint. The jabref software allows to manage a bibtex file which includes to add new entries and push the bibtex key to the lyx software. Also it provides the ability to search for dubplicates and can search in the database for any field. This makes jabref a powerful bibliography manager which can be recommneded to latex and lyx users as well.
Unfortunately, it has little or no support for handling notes created by the user while he is reading documents. Suppose somebody has found an interesting pdf paper and would like to write down 3-5 important short sentences what was written in the article. The jabref software has similar to the bibtex standard a field “Note” which allows to formulate free text. In the screenshot the sentence “The quick brown fox jumps over the lazdy dog” was entered.
The problem is, that the field is only one under many. It is a detail feature within the bibtex ecosystem. It can't store bold formatting, it can store images, tables and it is not possible to link from one note to another. The chance is high that most users doesn't even know about this field, most bibtex database were created with additional notes.
On the other hand, for a single user who writes a paper it is very important to annotate a reference. It is the core element of active reading and nearly all common place books are created around personal notes of the users. It is unfair to blame the jabref software for the low quality notes field, because the underlying bibtex standard doesn't support it as well. A more realistic attempt to describe the situation is by recognizing that note taking was mostly ignored in the past. There are wonderful software programs available to format a document like latex and powerful frontends like lyx and jabref but what is missing is the ability to create a personal knowledge management database. The only program which goes in this direction is the emacs org-mode which was introduced in 2003. [1]
[1] Johnson, Timothy. "Emacs as a Tool for Modern Science." Johnson Matthey Technology Review (2022).