Answer : D : Both Statements are False.
Statement 1 : "In a lattice $L$, if each element has at most 1 complement then it is distributive."
This is False But the converse is True.
Many examples of lattices which have at most 1 complement for its every element but Not distributive could be given. A Simple one is as follows :
In the above lattice, Every element has at most one complement. Elements $B,C,D$ have $0$ complements whereas $A,E$ have $1$ complements(They are complement of each other). But this lattice is Not distributive as it has Diamond(or Kite) lattice as Sublattice.
https://math.stackexchange.com/questions/2814774/example-of-a-lattice-which-has-at-most-1-complement-for-its-every-element-but-it
Statement 2 : "A Sublattice of a complemented lattice is also complemented lattice."
This is also a False statement. Easiest counter example is the Diamond lattice itself. Diamond lattice is complemented lattice But It has a sublattice which isn't complemented.
For the above Diamond lattice, Subset {$A,D,E$} is a Sublattice Which is Not Complemented as $D$ doesn't have any complements in the Sublattice.
Moreover, there is a Result proven by Dilwaorth which states that "Every lattice is a sublattice of a lattice with unique complements." So, You could use this Result also to show that Statement 2 is False.
https://www.google.co.in/search?q=kite+lattice+in+discrete+mathematics&source=lnms&tbm=isch&sa=X&ved=0ahUKEwj08_Gd1NfeAhXJWysKHb1IAscQ_AUIDigB&biw=1366&bih=626#imgrc=XdZh5vyN_CI9nM:
https://en.wikipedia.org/wiki/Lattice_(order)#Sublattices
http://www.ams.org/journals/tran/1945-057-01/S0002-9947-1945-0012263-6/S0002-9947-1945-0012263-6.pdf
https://math.stackexchange.com/questions/2814774/example-of-a-lattice-which-has-at-most-1-complement-for-its-every-element-but-it
