The actress is perhaps best known for playing drug addict Rainie Cross in EastEnders, before she left the UK to pursue a Hollywood career last year.
Liz & Dick stars Lohan and Grant Bowler as film legends Elizabeth Taylor and Richard Burton, and focuses on the stars' two marriages.
Franks will portray Burton's first wife Sybil Williams, whom he divorced in 1963, the year before he first married Taylor. The couple had two daughters together.
The film's director Larry Thompson has praised Franks for her "emotionally charged" performance, reports The Sun.
Franks had previously said of her role: "It's fun playing Rainie drunk but I don't drink - so there's no chance of me having any before filming to help me out."
She has also starred in the likes of Family Affairs, Pulling and The Bill.
Liz & Dick is scheduled to premiere on November 3 on Lifetime in the US.