The license text just requires that the user "can" do it: "Accompany the work... with the complete machine-readable "work that uses the Library", as object code and/or source code, so that the user can modify the Library and then relink to produce a modified executable containing the modified Library." Interpreting that is a question for the court; I would speculate that manual instructions are probably good enough as long as you provide instructions that actually work.

You can read this in the license:

> The “Corresponding Source” for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities.

A good open-source (or even source-available) project will include all the necessary build scripts and instructions needed for rebuilding it anyway, and it will be portable enough that this process isn’t tied down to a non-public CI environment.

If you’re asking exactly how much of this you can legally get away with omitting from a project using an LGPL library, then (a) you’re clearly not interested in providing a good open-source project, and (b) you should probably consult a lawyer rather than looking for free armchair legal advice from the community that you’re trying to avoid contributing to.

Entirely outside of the licensing debate, if your project only builds on a specific CI that's a huge engineering red flag I'd say