"engaged in litigation" is correct and usable in written English.
You might use it to describe someone who is involved in a legal dispute. For example, "The company has been engaged in litigation with its landlord for the past six months."
He was engaged in litigation with the Bell people when he died.
Mr O'Brien has been engaged in litigation against Red Flag since 2015.
CBS and other networks hate it, and are engaged in litigation with Dish over it.
They are equally serious whether he currently in engaged in litigation before the judge or not.
Racine is already engaged in litigation with Trump because the president has sued the District over his hotel's tax bill.
In this record group are many of the papers generated by the attorneys and staff engaged in litigation.
Under the supervision of clinical professors, Clinic students engage in litigation before administrative agencies and courts on a range of matters.
Larry Schwartztol is Counsel at Protect Democracy, where he engages in litigation and other advocacy to defend and strengthen democratic norms and institutions.
One, Taxation With Representation Fund, was organized to promote TWR's goals by publishing a journal and engaging in litigation; it had tax exempt status under § 501(c)(3).
As the Reuters legal blogger, Alison Frankel, put it last June, when Posner rendered his withering decision, "Would any rational economic actor engage in litigation under those terms, spending millions on an apparently impossible quest" to satisfy Posner's damages criteria?
The lawyers retained the right to sue on behalf of their clients over eligibility for specific benefits, but they were prohibited from engaging in "litigation, lobbying or rule-making involving an effort to reform a federal or state welfare system".
