How does Photoshop convert LAb to RGB values?

I'm working on a project and the only way to obtain RGB or LAB values is my using the color picker. I don't want to have to do that manually everytime i need an lab to be converted to a photoshop RGB. I need to know how that is computed.

First, there's no such ting as "RGB" to convert to, only specific RGB color spaces such as sRGB, Adobe RGB or ProPhoto. You get different values in all of them.
As it happens Lab values are always available through the Color Management Module. Lab is one of two profile connection spaces used in all color management operations (the other is CIE XYZ). For instance, as you view the image on screen the RGB values in the file are constantly calculated as document profile > Lab (or XYZ) > display profile.
These are complex calculations and good luck doing it manually. The easy way is to use the color picker.

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