Dear Sarah
it's currently just a holding page
I see, allgood i can setup some basic example's on a test site for you.
First Question:
I would love to know how to change the dropdown menu title to an image so I can use a burger and 'X' icon. Could you please advise?
If you wish to use Lay Theme's built in Burger Menu then you will have to create all Layout's within your Mobile Layout. If you do not wish to use only Mobile Layouts then it will need to be custom coded to appear on Desktop Layouts.
Here is a basic setup, a Sub-menu with three projects inside (please note: my "sub-menu" was created with the "custom-links" option, we will be using it's data-type later) :


I want to give this "Sub-menu" a custom class so i can easily target it. To do this I go into my Menu options and click "screen Options" in the right hand top corner:

Then i choose the Option "CSS Classes"

Now i can give my Sub-menu Title a CSS Class, for example custom-burger

Checking on the Front-end i can confirm that my Sub-menu now has the added class custom-burger
( right-click - inspect ):

We could use jQuery to replace text with image but for this we can make use of some simple css ( here the custom link comes in handy to specify ), (Code can be inserted into your Lay Theme website via > Lay Options > Custom CSS & HTML or > Customize > CSS:
https://laytheme.com/documentation.html#custom-css-styling
.custom-burger [data-type="custom"] { content: url(https://rickei3.dreamhosters.com/wp-content/uploads/2021/11/menu.png); }
https://www.w3schools.com/cssref/pr_gen_content.asp
The above code is replacing the text with an image defined by it's URL path. You can get url path of any image from your Media Library. > Appearance > Media >
Upload any image and then see it's details, in the bottom right corner you can copy the URL file path and insert it into the above code, replacing my example:

Your code may look like similar too this:
.custom-burger [data-type="custom"] { content: url(https://sarahswebsite/wp-content/uploads/2021/11/menu.png); }
Lets see the result, Closed sub-menu:

Open Sub-menu:

so now we need the final piece which it to make sure that the Burger is replace by an 'x' when then sub-menu is open.
When the Sub-menu is 'open' a class is added called show-submenu-desktop
. We can take advantage of this for our 'X' button:

Here the code defines that only when this class is added (meaning the sub-menu is open) do we change the image.
.show-submenu-desktop [data-type="custom"] { content: url(https://rickei3.dreamhosters.com/wp-content/uploads/2021/11/close.png); }
This image is an 'x' remembering i took the URL file path and inserted into the code. Lets see the Result!
Submenu closed:

And sub-menu open:

I wont go into dimensions of the Image Sarah and will leave this up to you, this will be dependent on your design needs and how you want your site.
https://www.javatpoint.com/how-to-change-image-size-in-css
Questions 2:
"Is there a way to adjust (increase) the line spacing between drop down menu items? I tried to change the text format but it is still tight. (screenshot attached)"
You can adjust the space between menu-items via > Customize > Menu styles > Submenus > Space between submenu points >
Here i have exaggerated 40px to show you:

Hope this helps you Sarah, the finer tuning will need to be done by you, but this is one way of changing the sub-menu into a "burger-menu" while still using Desktop Layouts.
Best wishes & have a wonderful day 🌻
Richard