Is all lingerie with lace really made out of lace?

No. The word "lace" is used very loosely these days. Only Leavers lace is "real" lace. Leavers lace is woven and contains a multitude of knots. "Fake" lace is knitted or even obtained by using chemicals.  It is of lesser quality than Leavers lace by far. The knitted lace easily unravels and is also substantially cheaper because its production is much faster. Other types of "fake" lace are obtained by using a mix of silk, vegetal fabrics and a chemical solution.  The fabric is immerged into the chemical solution in which the vegetal fabrics are dissolved, thereby leaving only that part of the fabric representing the "lace" motif.

Another point to note is that generally, "fake" lace is produced in countries that do not respect workers' rights or human rights.