If you are looking specifically for the Tiffany Lucida cut + setting, it is available only from Tiffany's.
Price wise, you would have to enquire at Tiffany's. Since there are no other suppliers of Lucida cut diamonds, what they quote would be pretty much what you have to pay.
If they have something within your wish list in Singapore, they will be able to let you have the price immediately. Otherwise, they will source it from their inventory and, if available, revert within a couple of days on the price and bring it into Singapore if you are keen. I have found the Raffles Hotel outlet to be more cosy.
Finding an exact 1.00 carat is unusual. You are more likely to find something that is 1.00 +/- 0.05. However, do bear in mind that there is a significant price hike once a diamond hits the magic 1.00 mark. Hence, a 1.00 carat would cost more than a 0.98 carat on a per carat basis although there is a neglible size difference.
On the other hand, if you are willing to consider something that looks similar to a Lucida on a Lucida type setting for a lower price, you should do a search on "Lucida" and "Singapore" on this forum to learn more. Based on what I have read, those keen on a Lucida type cut and setting have been able to obtain a Lucere cut diamond on a Vatche X prong platinum setting for a similar look. However, whether this would suit you or the love of your life is very personal and subjective.
"Mercier" a Singapore based member in the jewellery trade, started this interesting thread on Singapore jewellers: https://www.pricescope.com/community/threads/diamonds-and-jewelry-in-singapore-where-who-and-what.6110/
For more information on diamonds, do click on the "Tutorial" section of this website. You could also try http://
www.niceice.com or http://www.goodoldgold.com to learn more about diamonds. While initially overwhelming, there are tons of background information.
Have fun in your search