Hi Prem -
Welcome to My Swiss Alps-
it looks like you have some worthwhile plans.
To better understand the travel timing, take a look at the timetable, and a map.
Please be sure to read the instructions page.
Zoom in and you can see the train lines.
To meet your goals, you will need at least a couple of things.
One is completely under your control, the other ...partially.
1.- Luzern -
In order to visit the two mountains near Luzern, not to mention sight seeing, you will need more than part of the 19th. On balance, you'll be better of if you stay in the region on the morning of the 20th, and don't go to Zürich until late in the day. Of course, if you have specific goals in Zürich, then they would take precedence.
Luzern has a lot more scenery than Zürich.
This trip is highly dependent on decent weather. Heavy clouds at higher elevations can make the highest part of the trip pretty much useless, unless you like to pay a lot to see the inside of some clouds.
Keep track of the local weather and be flexible on your amount of time in the Jungfrau region. Most people allow 2 or 3 days to better the chances of having a clear day. Clouds can gather in the afternoon, so the morning is often a better time to go up to the Jungfraujoch.