As David points out the original example is uncommon both regarding ties
and slurs. I like to add another example which represent a more common
use of ties.
As you can see from the ly-file I first use a tie, then a slur, then a
double dot.
I think that you could get away with the second as a tie, mostly because
it uncommon to slur notes of the same pitch. But I don't think it is
preferred practise to use it this way. The double dot could be used, but
in contemporary notation I think a tie is preferred.
Peter Bjuhr