I believe it is by straws (lottery) for the SP and then the Reverse Order of the Results for the LP. Is that correct?
Yes to the first part and No to the second.
From the USFS Rulebook:
Rule 3322 There will be a random draw for starting order in the first segment of each
event.
Rule 3365
B. TV Rule
1. At the U.S. Figure Skating Championships only, for the
championship (senior) ladies, men's and pair’s free skate, and for
championship (senior) free dance events, the final draw group shall
consist of:
Ladies and men: the last two warm-up groups will consist of not
fewer than 10 and not more than 12 competitors, the exact number
to be decided by the chief referee in consultation with the executive
director prior to the draw of the short program.
a. Starting order for the final two groups will be drawn in four
subgroups.
i. The top three finishers in the short program shall be the last
to skate in the final group and will be drawn from the first
subgroup.
ii. The fourth-, fifth- and sixth-place (or fourth- and fifth- place
if five in group) finishers in the short program will be the
first to skate in the final group, and will draw from this
second subgroup;
iii. The seventh-, eighth- and ninth-place (or sixth-, seventhand
eighth-place if five in group) finishers in the short
program will be the last to skate in the second-to-last group,
and will draw from this third subgroup.
iv. The 10th-, 11th- and 12th-place (or ninth- and 10th-place if
five in group) finishers in the short program will be the first
to skate in the second-to-last group, and will draw from this
fourth subgroup.
Pairs: four couples in the final group;
Dance: five couples in the final group.