use statements are executed at compile time. Think of

use Module LIST;
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as equivalent to:

BEGIN {
    require Foo;
    import Module LIST;
}
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(which, if you read the use manpage, it is.)

Your variable is getting set at runtime (it doesn't matter that it's in %ENV, that's just a coincidence). So you need to put it in a BEGIN block:

BEGIN { $ENV{'DTS_DIR'} = "/net/endeavor/users/DTS"; }
use lib qq($ENV{'DTS_DIR'}/common);
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