In an open letter to Meghan, 72 cross-party MPs pledged to use the "means at our disposal" to ensure the press accepts her right to privacy, shows respect and that its stories "reflect the truth".
Ms Lynch, who posted the letter on social media on Tuesday, told ITV News she was contacted by Buckingham Palace on Wednesday morning and asked if she was free to speak with the duchess.
The Labour MP said: "She was calling to thank myself and other women MPs for standing with her, sending the open letter to say 'we as women in public office absolutely understand what she is going through'.
"Although in very different public roles, we stand with her in solidarity to say we shouldn't be tearing down women in public life through the press or otherwise, and she was pleased to have seen that letter."
Ms Lynch, who said like Meghan she is also a "fairly new mum", said they also discussed the challenges of being in the public eye and managing childcare.
The open letter said the media had printed stories and headlines which had invaded the duchess's privacy and "sought to cast aspersions" on her character.
Ms Lynch said: "We were quite happy to stand with her and recognise that what she is going through has, on occasion, had xenophobic undertones.
"We are not happy about that at all. We stand with her on challenging that and we will look to do everything we can at this end if some of our national press do not have healthier, shall we say, interests in her life."