Edge cases:

• ";abc".LazySplit(";") will return an empty sequence. To match the behaviour of ";abc".Split(new char[] { ';' }) it should return the sequence { "", "abc" }.

• ";abc".LazySplit("") will return a sequence with a single item, the empty string. To match the behaviour of ";abc".Split(new char[] { }) it should return the sequence { ";abc" }.

Here's how I would suggest writing it.

First, deal with the empty separator

if (separator.Length == 0)
{
    yield return value;
    yield break;
}

Then have two variables, start and end that refer to the start and end of the substring we want to extract.

var start = 0;
for (var end = value.IndexOf(separator); end != -1; end = value.IndexOf(separator, start))
{
    yield return value.Substring(start, end - start);
    start = end + separator.Length;
}

yield return value.Substring(start);

To make your unit tests match the behaviour of string.Split, you also want to change LazyStringSplit to have

var expected = new[] { "ab", "cd", "", "" };

and LazyStringSplitEmptyString to have

var expected = new string[] { "" };

Edge cases:

• ";abc".LazySplit(";") will return an empty sequence. To match the behaviour of ";abc".Split(new char[] { ';' }) it should return the sequence { "", "abc" }.

• ";abc".LazySplit("") will return a sequence with a single item, the empty string. To match the behaviour of ";abc".Split(new char[] { }) it should return the sequence { ";abc" }.

Here's how I would suggest writing it.

First, deal with the empty separator

if (separator.Length == 0)
{
    yield return value;
    yield break;
}

Then have two variables, start and end that refer to the start and end of the substring we want to extract.

var start = 0;
for (var end = value.IndexOf(separator); end != -1; end = value.IndexOf(separator, start))
{
    yield return value.Substring(start, end - start);
    start = end + separator.Length;
}

yield return value.Substring(start);

To make your unit tests match the behaviour of string.Split, you also want to change LazyStringSplit to have

var expected = new[] { "ab", "cd", "", "" };

and LazyStringSplitEmptyString to have

var expected = new string[] { "" };

If you want to test that your implementation matches the behaviour of string.Split, I would suggest introducing a helper method for the tests. Something like

var expected = value.Split(new string[] { separator }, StringSplitOptions.None);
CollectionAssert.AreEqual(expected, value.LazySplit(separator));