Yes, it is possible to romance and marry Lydia in Skyrim24. Here's how:
To begin, you must complete the "Dragon Rising" quest for the Jarl of Whiterun, after which he will make you Thane and appoint Lydia as your Housecarl26.
You need to purchase an Amulet of Mara from Maramal in Riften. He can be found at the Bee and Barb or the Temple of Mara. You must also discuss marriage with him to trigger the marriage dialogue23.
Wear the Amulet of Mara and speak to Lydia. If the above conditions are met, a dialogue option "Interested in me, are you?" will appear26.
After agreeing to marry, speak to Maramal again to set the wedding date. Return to the Temple of Mara the next day to commence the ceremony24.
Some players appreciate Lydia's reliability as a follower, while others find her tendency to stand in doorways annoying2.
A mod called "Lydia Redefined" on Nexus Mods enhances Lydia's follower system, allowing you to control aspects of her AI and skills. This mod includes a spousal autonomy system that enables her to sandbox around your home, cook meals, or visit the market1. The mod also makes her attraction dependent on your actions1.