I have been researching for a long time now and just came across your old message. Actually Thomas was born in 1640 in Dedham Essex. (there is no new Braintree in UK).
My researches indicate. The original members of the family came to England with William the Conqueror or just after him. There was probably not a single ancestor but a group. They were French or Normans and the name comes probably from the Valley of the river Loue in west France. So they were the Louekyn.When they arrived in England they associated with Normans and were given land probably by the King. The name by around 1160, when we find the first real record of a John Lovekyn in Kingston on Thames near London was spelled as such. The 'v' substiting in latin for the French 'u'. The name was then pronounced as Loo-kin and the name still exusts in France today as Lucquin and is prom^nounced as above.
In England in the 12 th century thr Lovekyn family first settled in Kingston, and also in the counties of Essex, Kent. Shropshire and Yorkshire.
In the north od England the name by the mid 16th century was spelled as Lovekin. The name changed in north Essex in the early 1500s to Lufkin. About the same time in south Essex the name changed from Lovekyn to Luckyn then on to the names of today as Luckin, Lucking and Lukin. We also find some with the name Luskin and Lufkins.
I have researched the name since the early 1860s and for the last 7 years I have ben working on a history of the family but to date I am just reaching the year 1700.
I hope you find this intersting.