This concatenates your multiple lines and stores the single string in an array element:

#!perl

use 5.12.0;
use warnings;

my @joined = ();
my $index = 0;

while (<DATA>) {
    chomp;
    if (m{ \A line=ULMNm }msx && $. > 1) {
        ++$index;
    }
    $joined[$index] .= $_;
}

for (@joined) { say }

__DATA__
line=ULMNm  3  1fdy_07      N-ACETYLNEURAMINATE LYASE           user  
+ 1           3                                    
  RMSD =     1.06 A
  MATRIX:   -0.3862 -0.2080 -0.8987  0.6457  0.6347 -0.4244 -0.6587  0
+.7442  0.1108   -16.917   -91.429   -35.632  
                   D  47    SER       A  57    SER.?     
                   D  48    THR       A  56    THR.?     
                   D 165    LYS       A  33    LYS~?     
 
line=ULMNm  3  2tmd_00      TRIMETHYLAMINE DEHYDROGENASE        user  
+ 1           3                                    
  RMSD =     1.15 A
  MATRIX:    0.9011 -0.4313  0.0445 -0.1032 -0.3130 -0.9441 -0.4211 -0
+.8462  0.3266    52.913    23.262    25.449  
                   A 169    TYR       A  41    TYR~?     
                   A 172    HIS       A  95    HIS^?     
                   A 267    ASP       A  98    ASP~?
[download]

Outputs:

$ multiline_join_array.pl
line=ULMNm  3  1fdy_07      N-ACETYLNEURAMINATE LYASE           user  
+ 1           3                                      RMSD =     1.06 A
+  MATRIX:   -0.3862 -0.2080 -0.8987  0.6457  0.6347 -0.4244 -0.6587  
+0.7442  0.1108   -16.917   -91.429   -35.632                     D  4
+7    SER       A  57    SER.?                        D  48    THR    
+   A  56    THR.?                        D 165    LYS       A  33    
+LYS~?      
line=ULMNm  3  2tmd_00      TRIMETHYLAMINE DEHYDROGENASE        user  
+ 1           3                                      RMSD =     1.15 A
+  MATRIX:    0.9011 -0.4313  0.0445 -0.1032 -0.3130 -0.9441 -0.4211 -
+0.8462  0.3266    52.913    23.262    25.449                     A 16
+9    TYR       A  41    TYR~?                        A 172    HIS    
+   A  95    HIS^?                        A 267    ASP       A  98    
+ASP~?
[download]

I don't know what subsequent processing you want to do. I've just output each array element to the screen (say just tags on a newline).