TL;DR Use Duration, not LocalTime. See end of answer.
Question code is incorrect
Be aware that the 4th argument to LocalTime.of() is nanosecond, not millisecond, which you'd see if you print localTime:
System.out.println(localTime); // prints: 00:27:10.000000190
So you need to change your code to:
LocalTime localTime = LocalTime.of(0, minutes, seconds, milliseconds * 1000000);
System.out.println(localTime); // prints: 00:27:10.190
Using LocalTime
If you wanted the milliseconds value back, call getLong(TemporalField field) with ChronoField.MILLI_OF_SECOND:
localTime.getLong(ChronoField.MILLI_OF_SECOND) // returns 190
To gain total number of milliseconds, i.e. not just the milliseconds value, use ChronoField.MILLI_OF_DAY as argument:
localTime.getLong(ChronoField.MILLI_OF_DAY) // returns 1630190
Using Duration
However, since the input is named lapTime, the LocalTime class is not the right tool for the job. E.g. your code will fail if minutes >= 60.
The right tool is the Duration class, e.g.
Duration duration = Duration.ofMinutes(minutes).plusSeconds(seconds).plusMillis(milliseconds);
Or:
Duration duration = Duration.ofSeconds(seconds, milliseconds * 1000000).plusMinutes(minutes);
You can then get the milliseconds directly by calling toMillis():
duration.toMillis(); // returns 1630190
That works even if the lap time exceeds one hour, e.g.
String lapTime = "127:10.190";
. . .
duration.toMillis(); // returns 7630190
In Java 9+, you can get the millisecond part back easily, by calling toMillisPart():
duration.toMillisPart(); // returns 190