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Blue bordered cages are non-consecutive, fully ordered (NCFO)
Red bordered cages are consecutive, fully ordered (CFO)
The Old Lace is in the usual position.
There are two I-beam cages I-1 at R37C456 + R456C5 and I-2 at R456C37 + R5C456.

1. The only way to fit two CFO cages at R1C1 and R7C7 and the NCFO cage at R4C4 onto D\ R1C1 is for CFO cages = [234/678] -> NCFO cage at R4C4 = [159], placed for Old Lace, 1 placed for D/ R1C7, 5 placed for D/ R1C9 and both I-beam cages, 9 placed for D/ R3C9
1a. R5C5 = 5 -> R4C6 = {23}, R6C4 = {78} (cannot have 4,6 in NCFO cage at R4C6)
1b. Naked pair {37} in R2C2 + R8C8, CPE no 3,7 in R2C8 + R8C2
[I’ll omit routine CPEs, mainly those affecting “zero” cells, until they become useful.]

2. There are two other NCFO cages on D/ at R1C9 and R7C3 -> 1 in R1C9 or R7C3, no other 1 on D/ R1C9
2a. 9 in R3C7 or R9C1, no other 9 on D/ R1C9
2b. NCFO cage at R1C9, R2C8 = {46}, R1C9 = {1234}, R3C7 = {6789}
2c. NCFO cage at R7C3, R8C2 = {46}, R7C3 = {1234}, R9C1 = {6789}
2d. Naked pair {46} in R2C8 + R8C2, locked for D/ R1C9

3. CFO cage at R5C9 = [234/345/456/678/789] (cannot be [123] which clashes with R1C9) -> R6C9 = {23467}, R7C9 = {34578}, R8C9 = {45689}
3a. Killer pair 4,8 in CFO cage and R9C9, locked for C9

4. CFO cage at R7C8 = [12/23/45/56/67/89], no 3,7,9 in R7C8, no 1 in R8C9

5. 4,6 in N5 only in R46C5 + R5C46, R5C46 = R37C5 (Old Lace property) -> 4,6 must be in R3467C5, locked for C5
[Now the first key step …]
5a. 4,6 in N5 only in R46C5 + R5C46, R46C5 = R5C37 (Old Lace property) -> 4,6 must be in R5C3467, locked for R5, clean-up: no 5,7 in R6C9, no 6,8 in R7C9

6. 4 in C9 only in CFO cage at R5C9 = [234/345] or in R9C9 -> CFO cage at R7C8 = [12/23/56/67/89], no 4 in R7C8, no 5 in R8C9
6a. 8 in C9 only in CFO cage at R5C9 = [789] or in R9C9 -> CFO cage at R7C8 = [12/23/56/67], no 8 in R7C8, no 9 in R8C9
6b. Killer pair 2,6 in R7C7 and CFO cage at R7C8, locked for N9

7. CFO cage at R7C7 = [234] => CFO cage at R5C9 = [789] or CFO cage at R7C7 = [678], CPE no 7 in R456C8 + R8C9, clean-up: no 6 in R7C8

8. CFO cage at R7C7 = [234] or CFO cage at R7C7 = [678] => CFO cage at R5C9 = [234/345], CPE no 3 in R456C8 + R8C9, clean-up: no 2 in R7C8

9. CFO cage at R7C7 = [234] => CFO cage at R5C9 = [789] or CFO cage at R7C7 = [678] => CFO cage at R7C8 = [12] => CFO cage at R5C9 = [345]
-> CFO cage at R5C9 = [345/789], no 2 in R5C9, no 3 in R6C9, no 4 in R7C9

10. 1 in I-1 only in R37C6, locked for C6
10a. 9 in I-1 only in R37C4, locked for C4

11. 1 in I-2 only in R6C37, locked for R6
11a. 9 in I-2 only in R4C37, locked for R4

12. CFO cage at R7C7 = [234] => CFO cage at R7C8 = [56] or CFO cage at R7C7 = [678] => CFO cage at R5C9 = [345]
-> 5 must be in R7C89, locked for R7 and N9

13. 7,8,9 on D/ R1C9 only in R3C7 + R6C4 + R9C1, CPE no 7,8,9 in R3C1 + R9C7 using D\ R3C9

[Now the forcing chains seem to get a bit longer and were harder to find.]
14. CFO cage at R7C7 = [234] => R9C7 = 1 => R5C8 = 1 (hidden single in N6) => R6C3= 1 (hidden single in R6) => R1C1 = 1 (hidden single on D/ R1C9) or CFO cage at R7C7 = [678] => CFO cage at R5C9 = [345], CFO cage at R7C8 = [12] => R1C1 = 1
-> R1C1 = 1, placed for D/ R1C9
also 1 in R7C8 + R9C7, locked for N9

15. 1 in N9 only in R7C8 => R3C6 = 1 (hidden single in C6) or in R9C7, placed for D\ R3C1 -> no 1 in R3C1

16. CFO cage at R2C1, no 9 in R2C1, no 1 in R3C2
16a. 1 in N1 only in R2C13, locked for R2
16b. R3C6 = 1 (hidden single in N2)

[And the final breakthrough, which has been available for some time but I’ve only just found it.]
17. 8 on D/ R1C9 only in R3C7 + R6C4 + R9C1
R3C7 = 8 => R3C3 = 4, placed for D\ => R9C9 = 8 or R6C4 = 8 => R6C9 = 4 or R9C1 = 8 => R3C7 = 9 (hidden single on D/ R1C9) => R7C4 = 9 (hidden single in C4) => R7C9 = 5
-> CFO cage at R5C9 = [345], 5 placed for D\ R1C3, CFO cage at R7C8 = [12], CFO cage at R7C9 = [678], CFO cage at R1C1 = [234]
[Cracked. The rest is fairly straightforward.]

18. CFO cage at R2C1 = [67/78/89] (cannot be [56] which clashes with R3C1), no 1,5 in R2C1, no 5,6 in R3C2
18a. R2C3 = 1 (hidden single in N1), R2C9 = 9 (hidden single in C9)
18b. R9C1 = 9 (hidden single on D/ R1C9)
18c. Naked pair {34} in R9C78, locked for R9 and N9 -> R8C7 = 9
18d. R5C8 = 9 (hidden single in N6), R4C3 = 9 (hidden single in N4)

19. 4 in R5 only in R5C46, locked for N5
19a. R7C5 = 4 (hidden single in C5), placed for D\ R3C1 and D/ R3C9 -> R9C7 = 3, placed for D\ R3C1, R9C8 = 4

20. R2C8 = 6, placed for D/ R1C9, R3C9 = 7, placed for D/ R3C9, R3C7 = 8, placed for D/ R1C9, R5C7 = 2, placed for D\ R1C3 and D/ R3C9, R6C8 = 8, placed for D\ R1C3, R4C6 = 3, placed for D\ R1C3 and D/ R1C9, R3C5 = 6, placed for D\ R1C3 and D/ R1C7, R1C3 = 7, placed for D\ R1C3, R5C3 = 8, placed for D/ R1C7 and D\ R3C1, R4C8 = 5, placed for D/ R3C9

and the rest is naked singles, without needing to use the diagonals.

I'll rate my walkthrough at Hard 1.5 because the final forcing chains were longer and harder to spot.

All of my forcing chains are probably equivalent to "fish", although I don't know anything about "fish" beyond X-Wings and basic Swordfish/Jellyfish so don't know which "fish" they are.