GREAT question - Reports of the benefits of garlic are everywhere. It has been used for a very long time in herbal and folk medicine. And there is truth there.
But hard research studies, including vehicles for delivery of the benefits to the lungs and dosage, are missing in every case.
Here are some articles to dive into for a better understanding, some are easier reading than the others.
This has a great graphic showing the benefits of allicin in the body:
https://www.scientificarchives.com/article/allicin-as-an-adjunct-immunotherapy-against-tuberculosis
And one with an interesting explanation of how they built a model lung to test allicin:
https://www.spandidos-publications.com/10.3892/etm.2019.8387
Finally -
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8001868/
It unfortunately they reported "Allicin taken up by cells, or entering the bloodstream, reacts readily with GSH in competition with cysteine residues in proteins. For this reason, it is difficult to envisage being able to achieve a therapeutically relevant concentration of allicin in cells anywhere in the body by simply swallowing it. Furthermore, as mentioned in the introduction, allicin is an irritant which stimulates pain-sensing neurons, and self-medication has led to a spate of reports of self-inflicted harm."

So, Monday light reading for your entertainment.
My takeaway -
Inhaling garlic vapors may help by boosting antibiotic effectiveness, reducing their side effects and potentially having antimicrobial and anti-inflammatory actions.
Eating garlic, not so much - the helpful compounds are broken down by the body before the allicin reaches the lungs
Research is underway to develop a proper method of delivery and dosage.

Let's invite further evidence-based comments to our party!
Sue