How important is the quality of the negative for Lightroom processing (Path A) versus conventional printing (Path B)?

A good negative is a joy to work with. A bad negative must be salvaged, no matter which path you choose. If wet printing, you may find yourself tediously burning and dodging in order to milk just a tad more highlight detail from your nearly blocked up highlights. If scanning, you may have to tweak your scan settings, make multiple scans, and then combine the images later.

Point is, a blocked up highlight section causes you more work in either case. A bad negative is not easier to work with, simply the methods used to salvage it will change.

What are the limits of post-processing with Lightroom in Path A versus Path B with paper print? Can the quality of Lightroom output outperform the conventional printing?

The tools you are most likely to use in Lightroom and Photoshop came from techniques created in the darkroom. The quality differences cannot be compared unless we are talking print for print. Even then, turning a digital image into a print can be done via inkjet (dye or pigment) on a mind-boggling number of papers or chromogenic printing. This is a rabbit hole that many forum threads have gone down. I'll say simply: find what you like.

All that being said, there's a reason that people turn to editing in digital and that is because of immediacy of results and knowledge gaps in technique. Here are some examples of tools in Lightroom and their corresponding darkroom processes:

• Healing Brush/Spot Touch Tool: Very useful for cleaning up dust. The average image can probably be healed up in a minute or less. Spot touching a print requires a fine paintbrush, inks, and the ability to match colors or tones. You'll spend ~10-15min on the average print that needs just a bit of work, but before that, hours learning how to blend the right color or tone.
• Exposure/Contrast: In LR, simply move the sliders until satisfied, 5 minutes or less. In the DR, create test strips, develop them, dry them. Settle on ideal exposure. Create full size print or more test strips of key areas. Determine contrast needs. Repeat test strips using contrast filters. Print final. It is not uncommon to spend an entire day, if not longer, working on a single image.
• Distortion Correction: Simply click a button. In the DR, you'll have to get creative in tilting your enlarger or easel and/or manipulating the paper to curve instead of lay flat.
• Sepia Toning: In LR, apply the tone and play with some sliders for the application of it to highlights/shadows. In DR, the strength of the tone is related to time in bleach followed by time in toner. You'll end up chopping up the print you just spent a full day making in order to run test strips again. Once you've settled up on the right amount to tone, you'll have to re-print the original print and then apply the tone to it.

The list goes on. The point is, many of the tasks that would have taken months, if not years, to learn and then hours or days to apply in the darkroom take little to no learning at all in Lightroom (just click a button) and the application takes seconds to minutes.

I wouldn't judge either digital or analog in terms of overall quality or post-processing limitations. Just keep in mind that things in the darkroom take much, much longer to accomplish.