What the price has to cover
Your consultation time; the 2–3 hour session and the 1–2 hour touch-up; single-use supplies and pigment; premises, insurance, licensing and CPD; no-shows and corrections; and the years of training and practice that make it safe. A 'cheap' lip blush usually means one of those was skipped.
Structuring it
Most artists quote one inclusive fee covering session + one touch-up within a set window (e.g. 6–10 weeks), then a lower 'colour boost' price at 12+ months, and a separate higher fee for correction/neutralisation work because it takes more sessions and skill. Deposits (non-refundable, deducted from the total) reduce no-shows.
Market reality
Big-city experienced artists command four figures; newer artists in smaller markets charge less while building a portfolio. Undercutting drastically signals inexperience to good clients and attracts people who will also shop around for their correction. Compete on portfolio and trust, not price.