Thanks! how many would you do? the heating will be undercabinet heating.

I would put one light in each triangle to balance the lighting.

You really need to locate lighting based on a kitchen plan. Since you won't have upper cabinets because of the windows, all your counter task lighting will be accomplished by the recessed cans, although you could have a central decorative fixture for accent. They should be gimbals.

You may want to post a kitchen plan for review in a separate thread, as I estimate an 88" back wall for the sink, and once you factor in the angled counters on the sides you will be left with no room except for a sink base (e.g. dishwasher on the adjacent angled counter). Issues like that could be emblematic of some things you may have not thought about.

This is our layout ideas for lighting?

To answer the question just about lighting in the bay with the vaulted ceiling, I would place 4" gimbals like so (possibly 3" with shallower cone depending on what you want to spend). I might also place an LED strip uplight on top of a small cove behind the beam to light the ceiling and give some some general ambient light.

However, there's some things with the kitchen I would question to not be able to advise on the rest of the kitchen lighting. Like the distance from sink to anywhere. Circled in RED the upper wall cabinet under the beam, just so you can have symmetry around the stove (forced to be a shorter custom height). Dimensioned in GREEN the width of the aisle entering next to the long wing wall. And why are all the cabinets custom sizes - if you want them custom made, you can actually use standard cabinet dimensions that will allow much more flexiblilty for options, be less money initially, and be less headache in the future (fillers easily make up odd dimensions at the angles).

Thank you! we ordered the cabinets already so the plan is all set. Where you circled in green, the wall is being knocked out and where you noted in red, we agree. its just not shown on the plan bc we will order that cabinet after we know exactly how big the beam will end up. Any thoughts on lighting throughout the rest of the kitchen/dining room?

It's a little hard to read and tell what's going on in the drawing. It looks like there is a sort of tray ceiling around the whole area, and not sure about the height of Dining cabinets. But I'd probably have some accent cans on the Dining cabinets (either in the flat ceiling if tall cabs or in the angle if buffet cabs). Two each in front of stove wall and oven(?) wall, which would also wash the floor. Assume you want pendant (pendants - depending on fixture size) over island, that should bleed over the floor against the outer wall too as cans are probably not good there. Also assume you want Dining chandelier, that would bleed to the floor around the table.