let him | her | them + VERB

Point 124 C2 in CLAUSES/imperatives is defined as:

an imperative clause with ‘let’ + ‘him/her/them’ + base form of a main verb, to devolve responsibility.

Point 108 C1 is the same except the usage:

to give permission or allow something or instruct someone to allow something.

an iWeb search for:

. Let them|him|her _VV

1 . LET THEM KNOW 5249
2 . LET HIM KNOW 831
3 . LET HER KNOW 728
4 . LET THEM COOL 503
5 . LET THEM SEE 404
6 . LET THEM GO 403
7 . LET THEM SIT 388
8 . LET THEM DRY 387
9 . LET THEM GET 314
10 . LET HIM GO 290
11 . LET THEM TAKE 277
12 . LET THEM COME 240
13 . LET THEM HELP 224
14 . LET THEM MAKE 200
15 . LET THEM CHOOSE 182
16 . LET THEM PLAY 170

17 . LET THEM SOAK 153 B2 vocabulary

However, this seems to be just about cooking so allowing something is C1:

1 LET THEM SOAK FOR A FEW MINUTES 16
2 LET THEM SOAK FOR A FEW HOURS 13
3 LET THEM SOAK FOR A COUPLE OF 12

  Bend Bulletin
From popcorn to figgy pudding: Foods from holiday songs
Place the popcorn kernels in a water bath and let them soak for a few minutes.
22 Dec 2020

 

18 . LET HER GO 142
19 . LET THEM TRY 141
20 . LET THEM FEEL 138
21 . LET HIM TAKE 138
22 . LET THEM REST 127
23 . LET THEM TELL 127
24 . LET HIM GET 125
25 . LET THEM COOK 123
26 . LET HIM SEE 115
27 . LET THEM TALK 115
28 . LET THEM PICK 110
29 . LET THEM LEARN 109
30 . LET THEM DECIDE 108
31 . LET THEM USE 105
32 . LET HIM COME 95
33 . LET THEM THINK 94
34 . LET HIM MAKE 93
35 . LET THEM ENJOY 92
36 . LET THEM WORK 91