Can I use dc-to-dc converter to step up voltage of 20 3.7V 3Ah lithium-ion batteries connected in parallel?
No, this is not a good idea. 

First, 20 3Ah primary cells form a 60Ah battery, not 40. 

Second, up-converting voltage with 1:13 ratio will yield not a very efficient converter, losses go up as the duty cycle goes down.

Third, 20 cells in simple parallel won't last long, due to uneven wear of cell and overcharge of strong cells, unless the battery pack has individual cell management.

A better idea would be to re-built the battery into series configuration, 13S, and employ a BMS. But again, it will require a serious re-engineering.