Lunar Calculator cannot produce a proper simulation and calculation of the Moon's characteristics without the correct use of the right time.
Local time is read directly from your computer's clock and inserted into the "current time" boxes. You can choose to display the time in UTC (Coordinated Universal Time), or local. You can change this through the Edit --> Settings menu and window, or by double-clicking directly on the label "Loc" or "UTC":
A critical part of the calculation is how many hours offset your local time is from UTC. For example, Eastern Daylight Time (EDT) is -4 hours from UTC. That's right MINUS: you have to subtract four hours from UTC to get your local time. The example above shows that I am -6 hours from UTC. Under the Edit menu item, at the bottom there is a few status lines, one of which shows the offset from UTC. In the settings window you can specify a decimal number in case you are in a half-hour time zone.
Indicate your preference for time output throughout Lunar Calculator. Even if you choose UTC, you still must enter your time zone offset, because Lunar Calculator reads your system time, then adds the offset to create UTC in the display. For example, if you choose Local time, and click on "Current Time" in the main window, you will see the current time used. If you choose UTC and you are at 21:00 EDT July 23, then Lunar Calculator will place 01:00 July 24 in the datetime box.
Most users will want this item checked on. This way you don't have to worry about changes from daylight to standard time. However if you are using Lunar Calculator to simulate views from distant locations you do not want to use the current PC timezone, but the one appropriate for the location.

Julian Date and Delta T
Astronomers use Julian Date (the number of days and fractions since year -4712) to avoid possible confusion over local time, plus it is simpler mathematically to manipulate the dates of events than to use year/month/day.
In "Astronomical Algorithms", Jean Meeus also uses "JDE" which is "ephemeris time" or "dynamical time", a timescale independent of Earth's variable rotation. For our purposes, this is interchangeable with "TT" or Terrestrial Time. All calculations in Lunar Calculator are made in JDE following Meeus, by first converting from local or UTC time. The difference between the two is called "Delta T":
Delta T = JDE - UTC
As Earth's rotation (generally) slows down due to tidal friction, leap seconds are added to UTC. The effect of this is to change Delta T on an almost annual basis by a second. In 1990 Delta T was +56.9 seconds, and in mid-summer 2003, DeltaT was 64.184 seconds.
You can specify Delta T directly in the Settings window. Otherwise Lunar Calculator uses various formulae in "Astronomical Algorithms" to estimate Delta T into the future or past. The current value of Delta T can be found in Sky & Telescope or in the RASC Observer's Handbook.
Please note that almanacs such as the Nautical Almanac use TT for their tables, so unless you are careful, the values shown by Lunar Calculator may appear to be in error. To check for yourself, you can set the software to calculate values for a specific TT, through the Utilities menu:

By clicking on the Edit menu, you can see that the status has changed:

and it shows JDE with an offset of 0 from UT. As well, the "Loc"/"UTC" label has changed to "JDE" to remind you that you are in a different time mode. You can double-click on the JDE label to get back to local time. Because you are now about 65 seconds difference from the earlier calculation, you should re-calculate the image to bring everything back to your normal time zone.