that you should take Lovenox starting as soon as you start any BCPs and well before transfer. For MTHFR you also need extra folic acid and vitamin Bs. Either make up the following yourself from OTC vits. or ask doctor to prescribe something like Folgard 2.2 or Metanx. Basically you need 5mg folic acid, 50mg B6 and 1mg B12 daily starting at least 2 months before cycling.
It is a rather old fashioned and very conservative approach to only mediate on high homocysteine, so I think it is right that you are adding Lovenox and extra vits. You may well not need aspirin as well though and I would discuss the benefits of this and when to take it as it is a powerful medication.