Lilly is the double-L spelling of Lily — ultimately from the Latin lilium (the lily flower) — symbol of purity in Christian tradition.
Lilly does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Lilly reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.