My parser may encounter \"2:37PM\" (parsed by \"H:mma\") or \"02:37PM\" (parsed by \"hh:mma\"). How can I parse both without resorting to a try-catch?
I receive an erro
You can use String#format with %02d on the hour portion of the String. This will pad the value with 0 until its size 2. We can then replace the original hour portion with the formatted portion.
        String timeLiteral = "2:37PM";
        String originalHour = timeLiteral.split(":")[0];
        String formattedHour = String.format("%02d", Integer.parseInt(originalHour));
        String result = timeLiteral.replace(originalHour, formattedHour);
You did say you wanted to parse the string. So you can do the following.
for (String s : new String[] { "02:37PM", "2:37PM" }) {
    DateTimeFormatter dtf = DateTimeFormatter.ofPattern("h:mma");
    LocalTime lt = LocalTime.parse(s, dtf);
    System.out.println(lt.format(dtf));
}
Prints
2:37PM
2:37PM
To my surprise, it looks like the answer was formatter "h:mma", which actually discerns correctly between one- and two-digit hour specifications and even catches technically dubious times like "02:38 PM" (which should probably not have a leading 0, but tell it to my data sources...)
You can create a string for the hours and have an if statement to check whether the hours is < 10 (single digit) then prepend "0".
First of all, the error you get is caused by the H in your pattern, which parses hours in 24-hour format and gets into trouble if you put an a (for AM/PM) at the end of the pattern.
You can use java.time to parse the Strings to LocalTimes using a DateTimeFormatter that considers both of the patterns:
public static void main(String[] args) {
    // define a formatter that considers two patterns
    DateTimeFormatter parser = DateTimeFormatter.ofPattern("[h:mma][hh:mma]");
    // provide example time strings
    String firstTime = "2:37PM";
    String secondTime = "02:37PM";
    // parse them both using the formatter defined above
    LocalTime firstLocalTime = LocalTime.parse(firstTime, parser);
    LocalTime secondLocalTime = LocalTime.parse(secondTime, parser);
    // print the results
    System.out.println("First:\t" + firstLocalTime.format(DateTimeFormatter.ISO_TIME));
    System.out.println("Second:\t" + secondLocalTime.format(DateTimeFormatter.ISO_TIME));
}
The output of this is
First:  14:37:00
Second: 14:37:00
But it turned out you only need one pattern (which is better to have than two in a DateTimeFormatter anyway) because the h is able to parse hours of one or two digits. So the following code produces exactly the same output as the one above:
public static void main(String[] args) {
    // define a formatter that considers hours consisting of one or two digits plus AM/PM
    DateTimeFormatter parser = DateTimeFormatter.ofPattern("h:mma");
    // provide example time strings
    String firstTime = "2:37PM";
    String secondTime = "02:37PM";
    // parse them both using the formatter defined above
    LocalTime firstLocalTime = LocalTime.parse(firstTime, parser);
    LocalTime secondLocalTime = LocalTime.parse(secondTime, parser);
    // print the results
    System.out.println("First:\t" + firstLocalTime.format(DateTimeFormatter.ISO_TIME));
    System.out.println("Second:\t" + secondLocalTime.format(DateTimeFormatter.ISO_TIME));
}