"Would it possible for example for me to request a copy of the deeds from the lender? "
Highly unlikely that they would have any interest in taking up your Deeds, copying everything and sending the copies on to you. Some banks will copy and furnish a specific document , if requested by the borrower.
And what is a copy of your Deeds going to show you anyway?
Things you can do now are:
1. Make sure your LPT is paid to date and be prepared to discharge next years also.
2. Make sure your service charge is paid to date.
3. If applicable, apply for a Certificate of Discharge/Exemption from NPPR - google that if you don't know what it is.
4. Read through any documentation you have from your Management Company for issues like fire safety problems and have the common areas been transferred.
But, really, you should check with your own solicitor - they all have their checklists that they can send you.
Far better than complete strangers on here offering suggestions.
mf