This is tricky question, gender correction - I don't think lilly came across this situation so we wouldn't have specific house for it. But its about physical appearance (1st house), self value (2nd), wishes (11th), and creation (5th) because you are creating something yourself rather than being born with it and well surgery (Mars).
So interesting to see how Mercury (your significator) changes signs into Capricorn which rules the 5th here. Moon, ruler of 11th, house of wishes in your 1st. Both these planets change signs (sign change here is the significant part of answer, i would think). Mercury moves out of its detriment in 6 units. Moon changes signs in 10 degrees and into Venus ruled Libra, how appropriate! Also Moon squares Mercury, so maybe that's when the process really starts.
So I think 6-10 years. But if you are already making preparations and are at that stage where you are ready for sex change then maybe its months. But I doubt it. It looks like years. I think you need to start taking hormones and live as a woman for a time being, grow breasts etc... before the ultimate operation can take place. This takes several years.