Hair gets more damaged as it gets older due to combing, brushing, shampooing, rubbing on fabrics, the elements (known as 'weathering') wearing away the protective cuticle. However colour treated hair is at greater risk of or more vulnerable to weathering, so any lightening done now will accelerate weathering as your hair ages.
There is no ideal time to damage hair with peroxide but it's fun (!) so I would do it whenever suits you. Do spend a few weeks babying your hair with proven ingredients like coconut oil and - if your hair is not coarse - hydrolysed protein treatments. These two are proven to protect from peroxide damage. Always run strand tests and patch tests, don't ever use your head as a laboratory.
Aftercare again coconut oil and hydrolysed protein, also ceramides, 18-MEA and panthenol. Regular deep conditioners may help your hair feel nice but most ingredients will not patch repair or penetrate it's just a cosmetic effect. Also protect your hair religiously from UV light - wear a close weave hat or scarf, UV Buff.
You might consider switching from shea butter which does not penetrate but may block other useful ingredients from contacting the hair to a penetrating oil or butter like palm kernel, babassu, tucuma - these are all rich in lauric acid like coconut oil.
Good products include (use as a leave in so the actives can work/ no waste)
- Komaza Care Matani repair treatment spray (ceramides, protein, panthenol)
- Komaza Care Matani leave in conditioner (ceramides, protein, panthenol, natural oils)
- Scientific Essentials hair conditioner (18-MEA, protein, panthenol)
- any cheap pure coconut oil.