This is a job for an array of arrays.
Objective C
int[][] map = new int[26][];
map[0] = {B0000000, B0000000, B0000000, B0000000, B0000000}; // Letter "A"
map[1] = {B1111111, B1001001, B1001001, B0110110, B0000000}; // Letter "B"
... Populate the array ...
To do the lookup, get the ASCII value of the upper-case character (which will be from 64 to 90) and subtract 64, and use that as your array index:
char c = 'B';                   // char can be treated as an int
int index = toupper(c) - 'A';   // See the link above for an explanation
int[] result = map[ascii];      // Returns the map for "B"
Obviously, to finish this off, you'd need to loop over all chars and copy each result to your output.
NSString *myString = [NSString stringWithString:@"Tanner"];
unichar c;
for(int i=0; i<[myString length]; i++) {
    c = [myString characterAtIndex:i];
                                    // char can be treated as an int
    int index = toupper(c) - 'A';   // See the link above for an explanation
    int[] result = map[ascii];      // Returns the map for "B"
    
    ... Append the result to a list of results ...
}
Please excuse any Objective-C syntax issues, the question is tagged C#, so I had to adapt to Objective-C.
Update: C#
This is way easier in C#.  The concept remains the same, but the code is much neater.
public static class Lights
{
    public static byte[] Encode(string input)
    {
        // Convert to ASCII values, get the map, and flatten it:
        return input.ToUpper().SelectMany(c => map[c-65]).ToArray();
    }
    
    // Note: C# does not have Binary Literals, so here's an alternative:
    private const byte B0000000 = 0, B0000001 = 1, B0000010 = 2, B0000011 = 3, B0000100 = 4, /* ETC */ B1111111 = 127, B1001001 = 73, B0110110 = 102, B0111110 = 126, B1000001 = 129;
        
    // Create the map:
    private static byte[][] map = new []{
                    /* A */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* B */ new[]{ B1111111, B1001001, B1001001, B0110110, B0000000 },
                    /* C */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* D */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* E */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* F */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* G */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* H */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* I */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* J */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* K */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* L */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* M */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* N */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* O */ new[]{ B0111110, B1000001, B1000001, B0111110, B0000000 },
                    /* P */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* Q */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* R */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* S */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* T */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* U */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* V */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* W */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* X */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* Y */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                    /* Z */ new[]{ B0000000, B0000000, B0000000, B0000000, B0000000 },
                };
}
Here's how to get the results:
byte[] lights = Lights.Encode("BOB");
A couple of cool things to note: C# lets you iterate a string as if it was a char array, and it lets you perform char math, so the code is super-simple.  Yay!