You are absolutely right!
Removal of setting LD_LIBRARY_PATH in the aforementioned tests made them passing. The fix I used is below.
Thank you!
 
--Serge
diff --git a/tests/asm-tst4.c b/tests/asm-tst4.c
index 54d054c..ffea204 100644
--- a/tests/asm-tst4.c
+++ b/tests/asm-tst4.c
@@ -101,8 +101,7 @@ main (void)
     }
 
   if (result == 0)
-    result = WEXITSTATUS (system ("\
-env LD_LIBRARY_PATH=../libelf ../src/elflint -q asm-tst4-out.o"));
+    result = WEXITSTATUS (system ("../src/elflint -q asm-tst4-out.o"));
 
   /* We don't need the file anymore.  */
   unlink (fname);
diff --git a/tests/asm-tst5.c b/tests/asm-tst5.c
index 2a8b3f0..c5f13c0 100644
--- a/tests/asm-tst5.c
+++ b/tests/asm-tst5.c
@@ -113,8 +113,7 @@ main (void)
     }
 
   if (result == 0)
-    result = WEXITSTATUS (system ("\
-env LD_LIBRARY_PATH=../libelf ../src/elflint -q asm-tst5-out.o"));
+    result = WEXITSTATUS (system ("../src/elflint -q asm-tst5-out.o"));
 
   /* We don't need the file anymore.  */
   unlink (fname);
diff --git a/tests/asm-tst6.c b/tests/asm-tst6.c
index bd6a71d..548e87c 100644
--- a/tests/asm-tst6.c
+++ b/tests/asm-tst6.c
@@ -147,8 +147,7 @@ main (void)
     }
 
   if (result == 0)
-    result = WEXITSTATUS (system ("\
-env LD_LIBRARY_PATH=../libelf ../src/elflint -q asm-tst6-out.o"));
+    result = WEXITSTATUS (system ("../src/elflint -q asm-tst6-out.o"));
 
   /* We don't need the file anymore.  */
   unlink (fname);