Answering your question, normally Lightning and Fire will phase through eachother with no interaction whatsoever. However, some Fire and Lightning jutsus are so condensed, that they exhibit solid-like behaviour, so under the right circumstances they will clash with one another.
Here's a situation like that which happened in my Sensei test -
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My Flame Rasengan vs Dante's Chidori True Spear
(Raiton no Jutsu) - Lightning Release Technique
Rank: D
Type: Offensive
Range: Short - Mid
Chakra cost: 10
Damage points: 20
Description: The user will manipulate their chakra to create small bolts of lightning to attack their target.
Alright, now we will begin with the basic techniques of Lightning Release. Come over here and stand right next to me, cup both of your hands together, but leave a substantial space in between them, as if you're gripping a small spherical object like a ball. Focus your raiton chakra to this location, envision high frequency chakra being generated in between your palms and attempt to tame this wild force of nature, making sure it doesn't get the better of you. Once you stabilize the small amount of lightning chakra, connect your wrists before pushing your hands forwards and outwards to emit the chakra as a small bolt of lightning towards that central dummy five meters away from you, attempting to strike the bull's eye located on its chest.
Key Points: Pay close attention to every jutsu's range. This jutsu is short-ranged and won't travel very far. As a reference point, here's what the actual measurements are.
Short Range - 0 to 5 meters away from you
Mid Range - 5 to 15 meters away from you
Long Range - 15+ meters away from you
(Raiton: Raikou Oonami) - Lightning Release: Lightning Surge
Rank: D
Type: Offensive
Range: Short
Chakra cost: 10
Damage points: 20
Description: The user will concentrate their chakra and slam their hand on the ground to release a surge of lightning across the ground to the opponents feet to shock them.
After doing that, however many times it takes to be successful, I want you to concentrate your raiton chakra to your dominant palm and slam your hand upon on the ground. As your palm strikes the ground, release the built chakra as a surge of lightning which travels across the ground and direct it towards that group of interconnected dummies doused in water. If you do this correctly, the lightning should conduct into the first dummy and spread along all of the dummies, shocking them collectively.
Key Points: This requires you to slam your hand on the ground, and so can't be used in mid-air or without a solid surface to stand upon.