You will not make it to the sun.
To begin, while in the Border Ethereal, visibility is limited to 60 feet (DMG p48). So it is entirely feasible to navigate through a city on the Prime Material Plane while in the Border Ethereal. But navigating through large unpopulated areas (i.e. space) accurately with no way to check bearings would be extremely difficult to nigh on impossible.
Etherealness also has a duration of 8 hours. If you are a spellcaster with access to 9th level spell slots, you could have up to 24 hours of Etherealness active before needing a long rest. Assuming you take the Dash Action and have a standard speed of 30, you move at 60 feet per round/600 feet per minute/3600 feet per hour/86,400 feet per day. As moving vertically costs an extra foot per foot moved, you're effective per day distance you can travel is 43,200 feet. Converting to miles, we get 8.16 miles per day.
But that's combat speed. The fast travel pace from the DMG (p182) lists moving at a fast pace, you will cover 30 miles a day without exhaustion. Because of the difficulty in moving vertically in the Border Ethereal, let's say you can move 15 miles a day without risking exhaustion.
The sun is about 92.96 million miles from Earth (according to the first result from Google). The exact distance doesn't really matter, as a. we're discussing a D&D approximation of Earth, and b. the order of magnitude is so large. So lets do some rounding. Say your sun is 90 million miles away and you can travel 100 miles a day. It's still going to take you 2,465.75 years to get there.
So aside from needing to be suicidal enough to want to undertake this venture, and having a way to circumvent the food requirements, you need to live for far longer than any of the standard playable races.
But Liches be crazy, right?