First off, let's get the terms and concepts right...
CMYK, just like RGB, does not describe color.
CMYK is a composite of 4 greyscale (achromatic) images. Each greyscale image can represent 100 tones/levels of grey. The color that you see represented by a composite CMYK image is dependent on the hues used to print each component greyscale image. Change the hue of each component and the final color changes. The range of colors that can be represented using a CMYK model is dependent on the hues of the CMYK components, the observer, the substrate, and the illumination.
RGB is a composite of 3 greyscale (achromatic) images. Each greyscale image can represent 256 tones/levels of grey. The color that you see represented by a composite RGB image is dependent on the hues used to print each component greyscale image to a screen display. Change the hue of each component and the final color changes. The range of colors that can be represented using an RGB model is dependent on the hues of the RGB components, the observer, the display, and the ambient illumination.
CIE L*a*b*, on the other hand, is a 3 coordinate locational system for defining a color. If two measured samples have the same coordinate values then they are (theoretically) identical. The color identified using a CIE L*a*b* model is dependent on the instrument used to determine the coordinate values. I.e. Two different instruments can give two different coordinate values for the same sample.
Pantone is a proprietary custom color library. Each color in the library is defined by a recipe of specified ink/pigment components. I.e. to get a specific hue, you mix X parts of one ink with parts of other inks. AFAIK, Pantone includes CIE L*a*b* coordinates only as a convenience for color systems that use ICC profiles or LUTs to convert Pantone's library into various color models (RGB, CMYK, etc).
Below is part of the Pantone library that is licensed to RIP vendors:
In this image 021 Orange is highlighted and you can see the CIE L*a*b* values that Pantone has provided to a RIP vendor.
In the box is the same 021 Orange as represented in PhotoShop's Pantone color library that Pantone has provided to Adobe.
Notice that the CIE L*a*b* values are different.
Since the CIE L*a*b* values are different, the resulting RGB/CMYK values will also be different, and hence the resulting colors simulating the target 021 Orange will be different.
Pantone does alter the CIE L*a*b* values it licenses to third parties as time goes by. The third parties may or may not be up to date with implementing the different versions of Pantone's libraries, nor do they necessarily ensure that the libraries used in individual vendor's applications are the same.
Which may be the problem in the OP's case.