Actually, assuming Lucas is a first name, Lucas' and Lucas's are both grammatically correct. The answer depends on the style book you follow as far as punctuation.
For example, King James's is traditionally correct. And here is an example noted from a grammar school with the same name:
http://en.wikipedia.org/wiki/King_James%27s_Grammar_School,_AlmondburyAs shown with
The Elements of Style, be consistent. If you use Lucas', as opposed to Lucas's, then keep it that way in your writing. No switching. There may be some disagreement between journalistic or publishing style, such as between
The Associated Press Style Manual and
The Chicago Manual of Style, so be sure to follow the style the printing house wants.
Again, either is correct depending on the style book you follow.
Naturally, there are exceptions to the rule, such as with Jesus' name, but that's a whole 'nother can of worms.