Your lender's estimate is realistic for a smooth process, but I'd say don't lock yourself into that timeline. The 30-45 day window assumes everything goes right - your appraisal comes back at value, you have clean financials, no weird questions from underwriting. In reality, most people I know who've gone through this hit some kind of snag that adds a week or two.
The biggest variable is underwriting. That's where they dig into everything, and depending on your income sources, the property itself, or anything unusual on your credit, they might request extra documentation. Appraisals can also drag if the appraiser is backed up. You're already pre-approved which is good - that means they've already done a basic check - but full approval is a different animal.
One thing that helps: stay on top of your lender. Don't assume silence means things are moving smoothly. Check in every week or so and ask specifically where you are in the process. I've seen deals push past 60 days because someone wasn't following up and documents got lost in the shuffle. Keep your finances clean between now and closing too - don't take on new debt or make big purchases. That stuff can actually kill a deal even after approval.