Reference request: proof that if $L \in DCFL$, then $L \Sigma^* \in DCFL$
One of the early works on DCFL is Seymour Ginsburg, Sheila Greibach: Deterministic context free languages, Information and Control, Volume 9, Issue 6, December 1966, Pages 620–648, doi:10.1016/S0019-9958(66)80019-0

The paper has various closure properties, for instance closure under complement (mind that my old Hopcroft and Ullman book states ".. was observed independently by various people") and closure under quotient with regular languages. 

Closure of DCFL under concatenation with regular languages is the result you need, which is Theorem 3.3 from the paper.