One safety note because you mentioned microneedling and that the scalp was bleeding: do not apply lavender or any other essential oil to freshly microneedled, broken, inflamed, or infected skin. Essential oils can cause irritation or allergic reactions, and microneedling increases penetration. Wait until the skin has fully healed and follow your dermatologist's aftercare instructions.
Evidence-wise, lavender oil alone has not been proven to regrow human hair. The often-cited 1998 trial tested a blend of thyme, rosemary, lavender, and cedarwood in carrier oils, so it cannot isolate lavender's contribution. For optional cosmetic use on an intact scalp, a conservative adult starting point is about 1% (for example, 3 drops in 15 mL jojoba oil): patch-test the finished blend, leave it on for only 10-20 minutes at first, wash it out, and stop if irritation occurs. It should not replace diagnosis or established treatment.
I summarized the studies, their limitations, and dilution details here: [lavender oil for hair]( https://lavenderessentialoilbenefits.online/lavender-oil-for-hair/). Disclosure: this is a page I maintain. Wishing you a safe and useful follow-up with your doctor.