There is nothing magic about any sharpening angle. A lower angle is better until you cut something hard enough to bend your thin edge. This would be something really hard like bone or metal so I generally go thin for my usage.
I like to thin a blade by honing it at under 15 degrees. For your LST I would look at this angle as laying the edge on the hone and setting the angle by stacking a couple pennies barely under the spine of the blade. While honing the left side of the blade I would hold this angle by holding the blade with the ball of my thumb pressed against the spine to allow a 2-penny of thumb width exposed on the left side of the spine. I would hold the blade this way while I honed with the side of my thumb grazing the surface of the hone. I would hone this way till I felt a burr form along most of the right side of the edge. Then I would flip the blade over and use a 2-penny-width of the side of my index finger as a guide to hone the right side till I had a burr along the entire blade length.
At this point you have a rough edge at 10 to 15 degrees per side, but with a major burr. Removing the burr does not require holding a precise angle, but I like to do it at about twice the angle that I used to hone. This would be a 4 or 5 penny stack of tilt. Very lightly hone edge-forwards alternating left and right sides. Your inexpensive stainless may give you a stubborn burr, but expect to remove it with about 4 strokes per side.
Now you want to set your edge at a slightly higher angle than you used when you thinned the edge. Since you used a two penny stack to set that angle use a three penny stack (or 2 pennies and 1 dime) to set your finish bevel. You are going to do light strokes, edge forwards for this like you did for deburring. I would only use the thumb and index finger angle-guide trick for a couple strokes to get the idea. It is very clumsy and slow to flip from side-to side and hit the finger guides. Do use light alternate strokes for only a few more strokes than you did for deburring. You don't want to make this bevel wide. If you have a ceramic rod v-block sharpener it probably wouldn't hurt to do 2 or 3 light strokes per side at an angle of around 20 degrees per side.
PS. The way that I figure the angle is like this.
The blade is around .75" wide (guestimate). To achieve an angle of 15 degree I need to elevate the center of the spine of the blade by .75 x sine(15). This is .75 x (.259) according to the Windows calculator (in scientific mode). This is .194 inch. Since the blade is about .1 inch thick you have half of the thickness (.05 inch) of angle space if you layed the blade flat on the hone. So you only need to add (.194 - .05) of spacing. This is .144 inch. Pennies are about .06 inches thick (according to a place I found by Google, but I could have just measured a stack of 10 and divided by 10). So if I stack 2 pennies I will be puting .120 inch of space under the spine of the blade. This is a bit less than the .144 inch that would give me 15 degrees. So given the slop in the calculations and your ability to hone straight the 2 pennies will give you a little under 15 degrees.
