You may find Boyer-Moore algorithm useful here. Convert your list to an array and search. The algorithm code is taken from this post.
static int SimpleBoyerMooreSearch(byte[] haystack, byte[] needle)
{
    int[] lookup = new int[256];
    for (int i = 0; i < lookup.Length; i++) { lookup[i] = needle.Length; }
    for (int i = 0; i < needle.Length; i++)
    {
        lookup[needle[i]] = needle.Length - i - 1;
    }
    int index = needle.Length - 1;
    var lastByte = needle.Last();
    while (index < haystack.Length)
    {
        var checkByte = haystack[index];
        if (haystack[index] == lastByte)
        {
            bool found = true;
            for (int j = needle.Length - 2; j >= 0; j--)
            {
                if (haystack[index - needle.Length + j + 1] != needle[j])
                {
                    found = false;
                    break;
                }
            }
            if (found)
                return index - needle.Length + 1;
            else
                index++;
        }
        else
        {
            index += lookup[checkByte];
        }
    }
    return -1;
}
You can then search like this. If lbyte will remain constant after a certain time, you can just convert it to an array once and pass that.
//index is returned, or -1 if 'searchBytes' is not found
int startIndex = SimpleBoyerMooreSearch(lbyte.ToArray(), searchBytes);
Update based on comment. Here's the IList implementation which means that arrays and lists (and anything else that implements IList can be passed)
 static int SimpleBoyerMooreSearch(IList<byte> haystack, IList<byte> needle)
 {
    int[] lookup = new int[256];
    for (int i = 0; i < lookup.Length; i++) { lookup[i] = needle.Count; }
    for (int i = 0; i < needle.Count; i++)
    {
        lookup[needle[i]] = needle.Count - i - 1;
    }
    int index = needle.Count - 1;
    var lastByte = needle[index];
    while (index < haystack.Count)
    {
        var checkByte = haystack[index];
        if (haystack[index] == lastByte)
        {
            bool found = true;
            for (int j = needle.Count - 2; j >= 0; j--)
            {
                if (haystack[index - needle.Count + j + 1] != needle[j])
                {
                    found = false;
                    break;
                }
            }
            if (found)
                return index - needle.Count + 1;
            else
                index++;
        }
        else
        {
            index += lookup[checkByte];
        }
    }
    return -1;
}
Since arrays and lists implement IList, there's no conversion necessary when calling it in your case.
int startIndex = SimpleBoyerMooreSearch(lbyte, searchBytes);