Hi,
Using the file and the expected output you showed. Something like this could help:

use warnings;
use strict;

my $line_required;

while (<DATA>) {
    $line_required = $_ if /^LOC/;
    if (/tAaAt/i) {
        print $line_required, $_;
    }
}

__DATA__
LOC_Os01g01320.1 : PS00022 EGF_1 EGF-like domain signature 1.
    390 - 401  CaCtgCatGTgC                                           
+      L=(-1)
  1013 - 1024  CcCaaGgtGTtC                                           
+      L=(-1)
LOC_Os01g01320.1 : PS00099 THIOLASE_3 Thiolases active site.
    976 - 989  AAGTACCAgAaAgA                                         
+      L=(-1)
  1269 - 1282  AAAGACGGtAaAtG                                         
+      L=(-1)
  1390 - 1403  GAAGACCAtAgAcA                                         
+      L=(-1)
LOC_Os01g01320.1 : PS00197 2FE2S_FER_1 2Fe-2S ferredoxin-type iron-sul
+fur binding region signature.
  1052 - 1060  CTGAACTTC                                              
+      L=(-1)
LOC_Os01g01320.1 : PS00269 DEFENSIN Mammalian defensins signature.
    868 - 896  CaCgctg.CtgaccttGtCcaactacgaCC                         
+      L=(-1)
LOC_Os01g01320.1 : PS00956 HYDROPHOBIN Fungal hydrophobins signature.
  2248 - 2259  GAgCATTTaCCT                                           
+      L=(-1)
LOC_Os01g01320.1 : PS01177 ANAPHYLATOXIN_1 Anaphylatoxin domain signat
+ure.
    462 - 494  CCttGaacgcat.TCAaggaga...TatCtatggc.CC                 
+      L=(-1)
  1786 - 1817  CCtgGcgttgattTCAacg......AaaCttactctCC                 
+      L=(-1)
  2428 - 2461  CCatAtcttagt.GCTattggc...GcaCttatgtaCC                 
+      L=(-1)
LOC_Os01g01320.1 : PS50214 DISINTEGRIN_2 Disintegrin domain profile.
    340 - 425  GGTCATCATTTGATCACTGACAAATTTCCCaAATCCTCCGATTTCGtatgCACTG
+CATGT L=-1
 GCTACTGGGAaACTGATTTTGAGACC--------
    868 - 964  --------------CACGCTGctgaCCTTGTCCAactacgacCAACTGCATATCA
+TGaaa L=-1
 ctTCCCcaatGCAGTTAGTACGTGGAaatcttccaaATATTTCCCATTTGC--------
LOC_Os01g01320.1 : PS50842 EXPANSIN_EG45 Expansin, family-45 endogluca
+nase-like domain profile.
  1422 - 1494  CGATGAGTcTATaAGGGTTGATGAAATTGCCATCAACTACTCTGAAACTGGagaA
+TCTTT L=-1
 TGATAGaaGAGCT---------------------------------------------
  2712 - 2793  TGCCGCTTgTGTtgttcAGatggaAACTGGTTATATTAAGAGCAACATCACTaag
+catat L=-1
 tGCTCCTAAaTTATTTTATC-----CT---------------------------------
 ------------
LOC_Os01g01320.1 : PS50868 POST_SET Post-SET domain profile.
  1961 - 1977  ACATCCCGAATCAGAAG                                      
+      L=-1
LOC_Os01g01320.1 : PS51173 CBM2 CBM2 (Carbohydrate-binding type-2) dom
+ain signature and profile.
  2593 - 2703  ATAATTGCATTATATGAGGCATCATGTGAATGTGTATGGCTTCGCAgaatGGTTA
+ACCAC L=-1
 ATATTAACATCTTGT--------GGTATTGGTTcATTGGAATcacCTACCATTATCTAT
LOC_Os01g01320.1 : PS51364 TB TGF-beta binding (TB) domain profile.
[download]

perl -wne '$l = $_ if/^LOC/; print $l,$_ if/tAaAt/i' log_file_you_use.
+txt
[download]

LOC_Os01g01320.1 : PS00099 THIOLASE_3 Thiolases active site.
  1269 - 1282  AAAGACGGtAaAtG                                         
+      L=(-1)
LOC_Os01g01320.1 : PS50842 EXPANSIN_EG45 Expansin, family-45 endogluca
+nase-like domain profile.
 tGCTCCTAAaTTATTTTATC-----CT---------------------------------
[download]