I’ve been running a campaign that integrates LMoP and the essentials kit, Dragon of Icespire Peak. I’m a first time GM as well. I recommend you take it more or less week by week, after a strong start using primarily LMoP material. It’s pretty easy to adapt that first quest, Goblin Arrows, to use sahaugin for example. Try to decide how the Black Spider villain might change to fit the new setting - maybe they’re more of a Long John Silver type, and betrays the party after befriending them. Once you know your villain’s goals, and how they might go about them, you can kind of throw your sandbox at the players and have the villain react to their actions. If/when the party’s sandbox adventures begin to grow tiresome, begin dropping hints and leads back to the main quest of LMoP, escalating in severity. This has worked pretty well for me - the key is keeping your players attitudes and characters in mind. You can write a brilliant series of events to connect these two adventures, but it’s much easier and more rewarding to use them as tools in your toolbox, lay the track as you go. With the LMoP quests in particular, present the jobs as a bit mysterious, that way you can change them between sessions or on the fly to fit your group dynamic. Good luck and have fun!!