Using 9 speed Deore front shifter with 10 speed Ultegra front Deraileur I am trying to build a bike out of all the spare parts I have in my garage. I found a 3x9 Deore front shifter, 3x10 Ultegra front d and crankset. Would they work together?

By the way, I am building a 3x1 drivetrain, with a Shimano Alfine 20t chain tensioner.

Cheers!
Front derailleurs don't care what you have in back (as long as the chainline is within reason). So you can ignore what's going on behind the front derailleur.

In terms of matching shifter and derailleur, an indexed front shifter needs to match in terms of capacity (3x), make/series, and capacity (tip of the hat to @mikes).

Fortunately, the Deore and Ultegra front shift points are largely compatible even though one is from the mountain bike line (your Deore shifter), and the other from the road bike line (Ultegra f. derailleur and crankset). Because you're using an indexed front derailleur with a different series shifter, you may need to tweak the indexing a bit but you should be able to get them to work. Many people use MTB triple cranks on their road bikes because of the wider range available, although you're doing the opposite here.

Life was easier with friction shifters.