How many months would it take for a typical lung carcinoid to reach 1.4cm?

Depends: It depends if this is well, or a poorly differentiated tumor. Well differentiated tumors tend to grow much more slowly compared to poorly differentiated tumors. A 1.4 cm well differentiated tumor could grow over a period of at least a year.

35 years: Cancers start as one cell which divides into 2 and then each of those cells divide making 4, etc. So tumors double in size at a regular interval which is called the doubling time (dt).For one cell to grow to the point that it can be seen on a CT(1mm) takes 20 doubling times.) It takes 32 dt to reach 1.6 cm. The average dt for typical lung carcinoids is 400 days. 32 x 400=12800 days or 35 years