If you help yourself with a combination table like this -
https://commons.wikimedia.org/wiki/File:Normal_form_matrix_of_Rock-paper-scissors-lizard-Spock.jpg
I use 2 instead of -1 (0 - Tie; 1 - win per line, 2 - row)
Then your code will look like this:
var options=["Rock","Paper","Scissors","Lizard","Spock"]
var outcomes=[[0,2,1,1,2],[1,0,2,2,1],[2,1,0,1,2],[2,1,2,0,1],[1,2,1,2,0]]
function RPSLS(user){
var computer=Math.floor(Math.random()*5);
if (outcomes[user][computer]==0){alert("Tie");}
if (outcomes[user][computer]==1){alert("User Wins");}
if (outcomes[user][computer]==2){alert("Computer Wins");}
txt1.value=options[user];
txt2.value=options[computer];}
Then the HMTL part to output:
Please choose:<br>
<button onclick="RPSLS(0)">Rock</button>
<button onclick="RPSLS(1)">Paper</button>
<button onclick="RPSLS(2)">Scissors</button>
<button onclick="RPSLS(3)">Lizard</button>
<button onclick="RPSLS(4)">Spock</button>
<button onclick="RPSLS(Math.floor(Math.random()*4))">Random Game</button><P>
<textarea id="txt1"></textarea><textarea id="txt1"></textarea>