Convert LifeOnTheEdge to LifeOnTheSlope Your task here is to take a LifeOnTheEdge pattern and convert it to LifeOnTheSlope.
A LifeOnTheEdge pattern is composed of these four characters: |_L . A pattern corresponds to a certain arrangement of &quot;on&quot; edges in a square grid. The pattern is placed in the grid first with the characters in the cells, and each of the four letters specifies the state of the edges on the left and the bottom of that cell. | means the edge on the left is on, _ means the bottom edge is on, L means both of them are on and   means neither of them are on.
For example the following LifeOnTheEdge:
|_L
 |

translates to:
. . . . .
|   |
. ._._. .
  |
. . . . .

Your task is however convert it to LifeOnTheSlope. LifeOnTheSlope is a LifeOnTheEdge equivalent but only uses three symbols: /\ . You should rotate the pattern 45-degree clockwise, for example the above example translates to:
/

/\/
  \

This is code-golf, so shortest answer wins.
EDIT: You can have leading and/or trailing spaces/newlines as long as the output itself (somewhere on the screen) is correct.
Test Cases
Input:
|_L
 | 
Output:
 /   
     
 /\/ 
   \ 

Input:
 |
_L
L_|
L_|
L_|
L_|
 | 
 |
Output:
        / 
     /\/  
    /\ \  
   /\ \/  
  /\ \/   
  \ \/    
  /\/     
 /        

Input:
__ __ __ __   __ __   __
|  | | ||L_   |_ | || L_
L_ L_|_L|L_   L_|L_|L |

Output:
 /\                        
/  \                       
\                          
 \  /\                     
   /  \                    
   \  /                    
    \/  \                  
        /\                 
      \/ /                 
       \/ /\               
         /\ \              
         \ \               
          \                
                           
               /\          
              /  \         
              \ \          
               \/ /\       
                 /  \      
                 \  /      
                  \/ /     
                    /      
                    \  /\  
                      /\ \ 
                        \
```
JavaScript (ES6),  135 120  119 bytes
Saved 16 bytes thanks to @Shaggy!
Expects either an array of strings or a matrix of characters. Returns a matrix of characters.

a=&gt;[...a,...a[0]].map((_,y,b)=&gt;b.map((_,x)=&gt;'\\/ '[(c=(a[~(x-=y+a.length)&gt;&gt;1]||0)[x+y-~y&gt;&gt;1])=='_|'[x&amp;=1]|c=='L'?x:2]))

Try it online!